# C1 help

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I'm stuck on two questions; the first is:

The equation x²+3px+p=0 where p is a non zero constant, has equal roots.

Find the value of p. I substitued abc into b²-4ac=0 and got 9p²-4p=0.

I don't really know what to do next. I tried factorising but that gives me two different answers. p=0 or p=-4/9. The -4/9 seems more correct than 0 but it doesn't seem right. The final equation is supposed to have two roots and factorise. Can someone show me where I went wrong?

The next question is: f(x)=x²+4kx+(3+11k) where k is a constant

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²

It then says f(x)=0 has no real roots, find the set of possible values of k. How do I do this, I can't use the normal method can I? since there's no roots and they want a set of possible values.

Sorry for the length, any help is much appreciated.

The equation x²+3px+p=0 where p is a non zero constant, has equal roots.

Find the value of p. I substitued abc into b²-4ac=0 and got 9p²-4p=0.

I don't really know what to do next. I tried factorising but that gives me two different answers. p=0 or p=-4/9. The -4/9 seems more correct than 0 but it doesn't seem right. The final equation is supposed to have two roots and factorise. Can someone show me where I went wrong?

The next question is: f(x)=x²+4kx+(3+11k) where k is a constant

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²

It then says f(x)=0 has no real roots, find the set of possible values of k. How do I do this, I can't use the normal method can I? since there's no roots and they want a set of possible values.

Sorry for the length, any help is much appreciated.

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#2

(Original post by

I'm stuck on two questions; the first is:

The equation x²+3px+p=0 where p is a non zero constant, has equal roots.

Find the value of p. I substitued abc into b²-4ac=0 and got 9p²-4p=0.

I don't really know what to do next. I tried factorising but that gives me two different answers. p=0 or p=-4/9. The -4/9 seems more correct than 0 but it doesn't seem right. The final equation is supposed to have two roots and factorise. Can someone show me where I went wrong?

**Year11guy**)I'm stuck on two questions; the first is:

The equation x²+3px+p=0 where p is a non zero constant, has equal roots.

Find the value of p. I substitued abc into b²-4ac=0 and got 9p²-4p=0.

I don't really know what to do next. I tried factorising but that gives me two different answers. p=0 or p=-4/9. The -4/9 seems more correct than 0 but it doesn't seem right. The final equation is supposed to have two roots and factorise. Can someone show me where I went wrong?

Your solution p=-4/9 should be p=4/9 - Let me know if you can't find your mistake.

If p=4/9 then you have

Try multiplying this equation by 9 then you should find it easier to factorise.

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#3

**Year11guy**)

I'm stuck on two questions; the first is:

The equation x²+3px+p=0 where p is a non zero constant, has equal roots.

Find the value of p. I substitued abc into b²-4ac=0 and got 9p²-4p=0.

I don't really know what to do next. I tried factorising but that gives me two different answers. p=0 or p=-4/9. The -4/9 seems more correct than 0 but it doesn't seem right. The final equation is supposed to have two roots and factorise. Can someone show me where I went wrong?

We can discard the p=0

**Edit:**As notnek (PRSOM) said - you're told p is non-zero.

The next question is: f(x)=x²+4kx+(3+11k) where k is a constant

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²[/latex]

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²[/latex]

It then says f(x)=0 has no real roots, find the set of possible values of k. How do I do this, I can't use the normal method can I? since there's no roots and they want a set of possible values.

Sorry for the length, any help is much appreciated.

Sorry for the length, any help is much appreciated.

Then that something must be negative for no real roots, and that gives you the desired condition which you need to investigate.

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#4

(Original post by

The next question is: f(x)=x²+4kx+(3+11k) where k is a constant

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²

It then says f(x)=0 has no real roots, find the set of possible values of k. How do I do this, I can't use the normal method can I? since there's no roots and they want a set of possible values.

**Year11guy**)The next question is: f(x)=x²+4kx+(3+11k) where k is a constant

Express f(x) in the form (x+p)²+q where p and q are constants to be found in terms of k.

I assumed it meant complete the square so I did: (x+4k/2)²-(4k/2)²

It then says f(x)=0 has no real roots, find the set of possible values of k. How do I do this, I can't use the normal method can I? since there's no roots and they want a set of possible values.

Try correcting this part and post your working if you're still stuck.

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(Original post by

You subtracted (4k/2)² but forgot to add on (3+11k). Does this make sense?

Try correcting this part and post your working if you're still stuck.

**notnek**)You subtracted (4k/2)² but forgot to add on (3+11k). Does this make sense?

Try correcting this part and post your working if you're still stuck.

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#6

(Original post by

Wait, was I right to complete the square? If so, I thought to complete the square it is : (x+b/2)²-(b/2)² and you disregard c, or am I incorrect?

**Year11guy**)Wait, was I right to complete the square? If so, I thought to complete the square it is : (x+b/2)²-(b/2)² and you disregard c, or am I incorrect?

(x+b/2)²-(b/2)² = x² + bx + (b/2)² - (b/2)² = x² + bx

Your method will only give you x² + bx. So you're right that doing this will disregard c but why would you want to do that?

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(Original post by

Yes, completing the square is correct.

(x+b/2)²-(b/2)² = x² + bx + (b/2)² - (b/2)² = x² + bx

Your method will only give you x² + bx. So you're right that doing this will disregard c but why would you want to do that?

**notnek**)Yes, completing the square is correct.

(x+b/2)²-(b/2)² = x² + bx + (b/2)² - (b/2)² = x² + bx

Your method will only give you x² + bx. So you're right that doing this will disregard c but why would you want to do that?

I'm sorry, I'm lost. Starting from the original equation:

x²+4kx+(3+11k)

Completing the square would give (x+4k/2)²-(4k/2)² but you want me to add on (3+11k) but the question wants it expressed in the form (x+p)²+q where p and q are constants to be found in terms of k.

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#8

(Original post by

I'm sorry, I'm lost. Starting from the original equation:

x²+4kx+(3+11k)

Completing the square would give (x+4k/2)²-(4k/2)² but you want me to add on (3+11k) but the question wants it expressed in the form (x+p)²+q where p and q are constants to be found in terms of k.

**Year11guy**)I'm sorry, I'm lost. Starting from the original equation:

x²+4kx+(3+11k)

Completing the square would give (x+4k/2)²-(4k/2)² but you want me to add on (3+11k) but the question wants it expressed in the form (x+p)²+q where p and q are constants to be found in terms of k.

-(4k/2)^2 + (3+11k) is in terms of k so it's fine. You can simplify it though.

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Ok, so I got (x+2k)²-(2k)²+(3+11k). What steps do I take to find the set of possible values of k. Am I right in expanding and simplifying to get : x²+4kx+3+11k?

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#10

(Original post by

Ok, so I got (x+2k)²-(2k)²+(3+11k). What steps do I take to find the set of possible values of k. Am I right in expanding and simplifying to get : x²+4kx+3+11k?

**Year11guy**)Ok, so I got (x+2k)²-(2k)²+(3+11k). What steps do I take to find the set of possible values of k. Am I right in expanding and simplifying to get : x²+4kx+3+11k?

Have a look at then end of Ghostwalker's post for the next step.

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(Original post by

No because now you're back to where you started

Have a look at then end of Ghostwalker's post for the next step.

**notnek**)No because now you're back to where you started

Have a look at then end of Ghostwalker's post for the next step.

I just substituted the original equation into b²-4ac<0 since there's no real roots. I got k<-3 and k<1/4

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#12

(Original post by

I just substituted the original equation into b²-4ac<0 since there's no real roots. I got k<-3 and k<1/4

**Year11guy**)I just substituted the original equation into b²-4ac<0 since there's no real roots. I got k<-3 and k<1/4

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(Original post by

Your critical points have the right magnitude, but the wrong signs, and one should be ">"

**ghostwalker**)Your critical points have the right magnitude, but the wrong signs, and one should be ">"

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#14

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(Original post by

'Fraid not. They both have the wrong sign. Post some working if you don't see why, as you may have the initial inequality incorrect too.

**ghostwalker**)'Fraid not. They both have the wrong sign. Post some working if you don't see why, as you may have the initial inequality incorrect too.

16k²-12+44k=0 This simplifies to 4k²+11k-3=0. This factorises to:

(4k-1)(k+3) The solutions are -3 and 1/4. I don't really get what to do next.

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#16

(Original post by

Ok, if there's no real roots, then b²-4ac<0. I substituted in a,b and c so it's a=1 b=4kx c=(3+11k). This makes (4k)²-(4*1(3+11k). This simplifies to:

16k²-12+44k=0

**Year11guy**)Ok, if there's no real roots, then b²-4ac<0. I substituted in a,b and c so it's a=1 b=4kx c=(3+11k). This makes (4k)²-(4*1(3+11k). This simplifies to:

16k²-12+44k=0

The minus sign outside the brackets effects both the "3" and the "11k".

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(Original post by

Should be

The minus sign outside the brackets effects both the "3" and the "11k".

**ghostwalker**)Should be

The minus sign outside the brackets effects both the "3" and the "11k".

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#18

(Original post by

So, the answers K<3 or K>-1/4

**Year11guy**)So, the answers K<3 or K>-1/4

__and__k>-1/4 i.e it's in the interval (-1/4,3)

**Edit:**Corrected - thanks Mr M

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