Question

let k be an integer. if the equation kx^2+(4k-2)x+(4k-7)=0 has an integral root. find the sum of all possible values of k.

Answer 1

Consider the given equation $kx^{2}+(4k-2)x+(4k-7)=0$,

Since the given equation has integral root

Therefore the value of discriminant (D)=0.

The formula for discriminant (D) = $b^{2}-4ac$ = 0

$D = (4k-2)^{2}-4k(4k-7)$

$D=16k^{2}+4-16k-16k^{2}+28k$

$D=12k+4$

So, to have integral roots, the value of D will be equal to zero.

Therefore, D=0

12k+4 = 0

$12k = -4$

$k = \frac{-4}{12}$

$k = \frac{-1}{3}$

so, the value of k is $\frac{-1}{3}$

So, the sum of the values of k is $\frac{-1}{3}$.