Thread: Sum and product of roots (help)

1. Sum and product of roots (help)

Find the value of n in the equation 2x^2 -5(n-1)x +12=0 If two roots are consecutive.

The answer in the book is n= -1 , 3

2. Re: Sum and product of roots (help)

Let roots be alpha and alpha+1

Sum of roots = 5(n-1)/2 = 2*alpha + 1

Rearranging equation to have only n LHS, n = (2/5)(2*alpha + 1) + 1

Prod. of roots = alpha(alpha + 1) = 6

alpha^2 + alpha - 6 = 0

Quadratic formula, alpha = -3 or 2.

Subbing into n = ....

n = -1 or 3.

3. Re: Sum and product of roots (help)

is this the next step

( sub 2 into n )

2x^2+5x+12=0

=-5 root 5^2 - 4(2)(12)/4

=-5 root 25 -96/4

there is no solution

4. Re: Sum and product of roots (help)

Originally Posted by Saini
is this the next step

( sub 2 into n )

2x^2+5x+12=0

=-5 root 5^2 - 4(2)(12)/4

=-5 root 25 -96/4

there is no solution
Let n = 2

2/5 * (4 + 1) + 1

= 3

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