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i am having problem with one question on my exercise ,

Q the roots of the equation ax^2+bx+c=0 differ by 1. prove that b^2-a^2-4ac=0

pls help!!!

Q the roots of the equation ax^2+bx+c=0 differ by 1. prove that b^2-a^2-4ac=0

pls help!!!

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#2

(Original post by

i am having problem with one question on my exercise ,

Q the roots of the equation ax^2+bx+c=0 differ by 1. prove that b^2-a^2-4ac=0

pls help!!!

**Pearl1323**)i am having problem with one question on my exercise ,

Q the roots of the equation ax^2+bx+c=0 differ by 1. prove that b^2-a^2-4ac=0

pls help!!!

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um... i try k(x-alpha)(x-beta) which i know is not quite right

i don't get what differ by 1 actually want me to do1!!

i don't get what differ by 1 actually want me to do1!!

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#4

**Pearl1323**)

i am having problem with one question on my exercise ,

Q the roots of the equation ax^2+bx+c=0 differ by 1. prove that b^2-a^2-4ac=0

pls help!!!

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#5

(Original post by

um... i try k(x-alpha)(x-beta) which i know is not quite right

i don't get what differ by 1 actually want me to do1!!

**Pearl1323**)um... i try k(x-alpha)(x-beta) which i know is not quite right

i don't get what differ by 1 actually want me to do1!!

What are the two solutions to the quadratic equation in the question?

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#6

Look into the two roots from the quadratic equation & see what it means for the two roots to differ by 1.

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#7

(Original post by

if you need some help for homework help. i think this is very good site homeworkbazaar.co.uk

**homeworkbazaar**)if you need some help for homework help. i think this is very good site homeworkbazaar.co.uk

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#8

(Original post by

Look into the two roots from the quadratic equation & see what it means for the two roots to differ by 1.

**oniisanitstoobig**)Look into the two roots from the quadratic equation & see what it means for the two roots to differ by 1.

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#10

(Original post by

so it should be k(x-alpha) (x-beta-1) like that ?

**Pearl1323**)so it should be k(x-alpha) (x-beta-1) like that ?

k(x-alpha)(x-beta).

But since you know the roots differ by 1, you can (without loss of generality) assume beta = alpha+1, and so rewrite as

k(x-alpha)(x-alpha-1).

However, for this problem the method suggested by oniisanitstoobig is going to be easier.

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#12

(Original post by

so it should be k(x-alpha) (x-beta-1) like that ?

**Pearl1323**)so it should be k(x-alpha) (x-beta-1) like that ?

**there are 2 ways of doing this**

verification (very easy)

K(x-alpha)(x-alpha-1) = 0 (the k is not actually needed)

multiply out into a three term quadratic in x

plug the coefficients into the expression given and done

properly (a bit of algebra)

alpha + (alpha + 1) = -b/a

alpha(alpha + 1 ) = c/a

eliminate alpha between the 2 equations

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#13

(Original post by

verification (very easy)

K(x-alpha)(x-alpha-1) = 0 (the k is not actually needed)

multiply out into a three term quadratic in x

plug the coefficients into the expression given and done

properly (a bit of algebra)

alpha + (alpha + 1) = -b/a

alpha(alpha + 1 ) = c/a

eliminate alpha between the 2 equations

**TeeEm**)**there are 2 ways of doing this**verification (very easy)

K(x-alpha)(x-alpha-1) = 0 (the k is not actually needed)

multiply out into a three term quadratic in x

plug the coefficients into the expression given and done

properly (a bit of algebra)

alpha + (alpha + 1) = -b/a

alpha(alpha + 1 ) = c/a

eliminate alpha between the 2 equations

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#14

(Original post by

I've now posted this 3 times, but in this case, I think it's pretty clear the shortest answer is to just use the quadratic formula.

**DFranklin**)I've now posted this 3 times, but in this case, I think it's pretty clear the shortest answer is to just use the quadratic formula.

Once conceived indeed the workings are 2 lines..

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#15

(Original post by

it is indeed, but conceptually for a student the hardest approach.

Once conceived indeed the workings are 2 lines..

**TeeEm**)it is indeed, but conceptually for a student the hardest approach.

Once conceived indeed the workings are 2 lines..

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#16

(Original post by

I dunno, I think it's the obvious approach (it's what I'd expect 90% of non-FM A-level students to do).

**DFranklin**)I dunno, I think it's the obvious approach (it's what I'd expect 90% of non-FM A-level students to do).

**It only becomes unobvious when you're in the middle of a topic where the answer to everything is to express x^2+bx+c in terms of alpha and beta**.(most students which have knowledge of relationships between roots and coefficients as soon as "... roots differ by 1 ...", autopilot takes over )

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so that solution is :

(2alpha+1)^2-(alpha^2+alpha)-4(alpha^2+alpha) ?

(2alpha+1)^2-(alpha^2+alpha)-4(alpha^2+alpha) ?

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