Question

If one root of PX is equals to K square + 4 bracket close X square + 13 x + 4 k is reciprocal of the other then find the k

Answer 1

Answer

p(x) = (k^2 + 4)x^2 + 13x + 4k

Let zeroes = ą, 1/ą

Product of zeroes = c/a = 1

=> 4k/(k^2 + 4) = 1

=> k^2 + 4 = 4k

=> k^2 - 4k + 4 = 0

=> k^2 - 2k - 2k + 4 = 0

=> k(k - 2) - 2(k - 2) = 0

=> (k - 2) (k - 2) = 0

=> k = 2