Question

Find the value of k if the product of the roots of the quadratic equation
kx^2 + 4x + k^2 -21 = 0 is 4

Answer 1

Recall that for a quadratic equation that is in the form
x^2 + bx + c = 0
the sum of the roots is equal to -b, and
the product of roots is equal to c.
Therefore, we change the form of the given equation by this form,
kx^2 + 4x + k^2 - 21 = 0
x^2 + (4/k)x + k - 21/k = 0
The constant term here is k - 21/k. This is product of roots, which is equal to 4 (given in the problem). Then equate:
(k - 21/k = 4)*k
k^2 - 21 = 4k
k^2 - 4k - 21 = 0
(k + 3)(k - 7) = 0
k = -3
k = 7

Hope this helps~ :)