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Maths help

I need help approaching these types of questions because it comes up A LOT

the equation 2x² - 3x - (k+1) = 0, where k is a constant

Q) find the set of possible values for k (4) k has no real roots
(edited 7 years ago)
Reply 2
I'm assuming the question asks for the values of k such that the equation has distinct real roots, or equal roots.
If so just consider the discriminant, remember b24ac>0 b^2-4ac>0 for distinct real roots and b24ac=0 b^2-4ac=0 for equal roots (single root you may think of it as). In this case,a=2,b=3 a=2, b=-3 and c=(k+1) c=-(k+1) .
If this isn't the question then please say what the actual wording of the full question was.
Original post by samantham999
I need help approaching these types of questions because it comes up A LOT

the equation 2x² - 3x - (k+1) = 0, where k is a constant

Q) find the set of possible values for k (4)


As said above, we can't really determine any restrictions on kk until we have more information about the roots.

If 2 distinct real roots; then b24ac>0b^2-4ac>0

If 1 repeated real root; then b24ac=0b^2-4ac=0

If 0 real roots; then b24ac<0b^2-4ac<0

where a=2,b=3,c=(k+1)a=2, b=-3, c=-(k+1)
Original post by B_9710
I'm assuming the question asks for the values of k such that the equation has distinct real roots, or equal roots.
If so just consider the discriminant, remember b24ac>0 b^2-4ac>0 for distinct real roots and b24ac=0 b^2-4ac=0 for equal roots (single root you may think of it as). In this case,a=2,b=3 a=2, b=-3 and c=(k+1) c=-(k+1) .
If this isn't the question then please say what the actual wording of the full question was.


The question is listed above, to find values of k and it says k has no real roots.
Original post by RDKGames
As said above, we can't really determine any restrictions on kk until we have more information about the roots.

If 2 distinct real roots; then b24ac>0b^2-4ac>0

If 1 repeated real root; then b24ac=0b^2-4ac=0

If 0 real roots; then b24ac<0b^2-4ac<0

where a=2,b=3,c=(k+1)a=2, b=-3, c=-(k+1)



Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?
Original post by samantham999
Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?


The value of the discriminant tells us how many real roots there are, and vice versa, the amount of roots tells us conditions which must hold for the discriminant (the one's above). Then we can use it to construct an inequality in terms of kk and solve it.
Reply 7
Original post by samantham999
Sorry, I forgot to say...k has no real roots so its obviously 0 real roots but i don't really understand the above?


So you're finding the values of k so that the discriminant is strictly less than 0. Do you understand this part? Do you know why this is the case?
Original post by RDKGames
As said above, we can't really determine any restrictions on kk until we have more information about the roots.

If 2 distinct real roots; then b24ac>0b^2-4ac>0

If 1 repeated real root; then b24ac=0b^2-4ac=0

If 0 real roots; then b24ac<0b^2-4ac<0

where a=2,b=3,c=(k+1)a=2, b=-3, c=-(k+1)


yeah i thought to plug them in by labelling a,b and obviously c but how do you leave your answer?
Original post by samantham999
yeah i thought to plug them in by labelling a,b and obviously c but how do you leave your answer?


As an inequality with kk on one side and everything else on the other. The inequality is the range of values that k can take - as required by the question - in order to have no real roots.
Original post by RDKGames
As an inequality with kk on one side and everything else on the other. The inequality is the range of values that k can take - as required by the question - in order to have no real roots.


so i did (-3)² - 4x2-(k+1)

which leaves 9 - 8 + 4k - 4 ?

is this step wrong?
Original post by samantham999
so i did (-3)² - 4x2-(k+1)

which leaves 9 - 8 + 4k - 4 ?

is this step wrong?


Yes.

(3)24(2)[(k+1)]=9+4(2)(k+1)=9+8k+8(-3)^2-4(2)[-(k+1)] = 9+4(2)(k+1) = 9+8k+8
Original post by RDKGames
Yes.

(3)24(2)[(k+1)]=9+4(2)(k+1)=9+8k+8(-3)^2-4(2)[-(k+1)] = 9+4(2)(k+1) = 9+8k+8


why is -4x2 = -8 wrong?
Original post by samantham999
why is -4x2 = -8 wrong?


That's right, I just don't know where you pulled the "+4k-4" from.
Original post by RDKGames
That's right, I just don't know where you pulled the "+4k-4" from.


silly me. now i got 9+8k-8 BUT, is it +8 because there is a negative sign infront of the bracket like this: -8-(k+1) ?

the answer says 8k < -17

how do you get -17? -9 -8
(edited 7 years ago)
Original post by samantham999
silly me. now i got 9+8k-8 BUT, is it +8 because there is a negative sign infront of the bracket like this: -8-(k+1) ?


Sort of, it is hard to say from your specific working because you got distributed the negative weirdly, but be careful with the way you write them. The way you represented that would read as "minus 8 take away the quantity of k+1" which is not correct - it should be "minus 8 multiplied by the negative of the quantity k+1" so the negatives cancel and you get left with 8(k+1) hence +8. Just look at my working above.
(edited 7 years ago)
Original post by RDKGames
Sort of, it is hard to say from your specific working because you got distributed the negative weirdly, but be careful with the way you write them. The way you represented that would read as "minus 8 take away the quantity of k+1" which is not correct - it should be "minus 8 multiplied by the negative of the quantity k+1" so the negatives cancel and you get left with 8(k+1) hence +8. Just look at my working above.


I understand. Thanks so much! yeah, i really need to take care with my negative signs tbh -8-(k+1) because - is infront of the bracket and infront of 8 it cancels because you are multiplying

thanks! so when i get questions like this it will see whether it has real roots or not and then i choose from the formula thing you sent first?
Original post by samantham999
I understand. Thanks so much! yeah, i really need to take care with my negative signs tbh -8-(k+1) because - is infront of the bracket and infront of 8 it cancels because you are multiplying

thanks! so when i get questions like this it will see whether it has real roots or not and then i choose from the formula thing you sent first?


Essentially, yeah. Though you should probably understand where those specific restrictions come from.
Original post by RDKGames
Essentially, yeah. Though you should probably understand where those specific restrictions come from.


I will check out exam solutions for it thanks :smile:

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