Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

C1 - No real roots help!

Spongebob*No*Pants

Given that the equation:

x^2 - 2kx + k +6 = 0

has no real roots, find the possible values of the constant

K

I know no real roots =

b^2<4ac

but how do i apply it here?

Thanks, rep will be given :smile:

:smile:

Study Forum Helper

a=1

b=-2k

c=k+6

a = 1
b = -2k
c = k + 6

That help? :smile:

:smile:

callum Honisett

If there are no real roots

b^2 - 4ac .

(is less than zero)

Sub a,b and c then draw a graph if it will help you find the range of values ( b^2 - 4ac is less than 0 )

Spoiler

Graph? Why?

Spongebob*No*Pants

OP

Mr M

a=1

b=-2k

c=k+6

ahh okay lol
Thanks + rep for you :smile:

:smile:

No need for a graph if you can do it all alegebraically

Your expression you wrote is wrong.

It's b^2 - 4ac < 0

K must be greater than -3 and less than 2.

callum Honisett

Guinny

Graph? Why?

Drawing a graph hepls you to see the solutions toa qaudratic inequality. In my opinion.

DaveJ

Your expression you wrote is wrong.

It's b^2 - 4ac < 0

b^2 - 4ac < 0 \Leftrightarrow b^2 < 4ac

Spongebob*No*Pants

OP

so

[br]-2k < 4k +24

[br]-6k < 24

[br]k > -4[br]

Is that right? when you divide by a negative the more than sign changes the other way.
Thanks again

Rhys.

b^2 - 4ac < 0 \Leftrightarrow b^2 < 4ac

Oh... fair enough then. Never seen it written like that before.

OP: Find the discriminant, then factorise it. Sketch the graph, notice that the y values are less than zero between -3 and 2, and that's your answer. That's if I haven't made a mistake, and I probably will have made one somewhere...

Spongebob*No*Pants

so

[br]-2k < 4k +24

[br]-6k < 24

[br]k > -4[br]

Is that right? when you divide by a negative the more than sign changes the other way.
Thanks again

Yes - that's right. easy way to check, sub -4 into the discriminant and see if it = 0, then you can see that if K < -4 , than b^2 is smaller than 4ac

Spongebob*No*Pants

so

[br]-2k < 4k +24

[br]-6k < 24

[br]k > -4[br]

Is that right? when you divide by a negative the more than sign changes the other way.
Thanks again

...

(-2k)^2 < 4k +24

I would shift it all to the LHS, simplify and complete the square which would give the possible range for k

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