Question

If the sum of roots of the equation 3x2-(3k-2)x- (k-6)- 0 is equal to the product of its
roots, then find k.​

Answer 1

The general form of a quadratic equation is ax²+bx+c=0

Products of roots is c/a

Sum of roots is -b/a

On comparing the above equation with general equation we have

a = 3

b = -(3k-2)

c = -k+6

Now it is given that sum of roots and product of roots is equal

So,

-b/a = c/a

-b = c

-[-(3k-2)] = -k+6

3k+2 = -k+6

3k+k = 6–2

4k = 4

k = 1