Question

If alfa,bita are zeroes of the polynomial p(x)= 3x^2-12x k such that alfa-bita=2 then find the value of k.?

Answer 1

k = 9

Explanation:

quadratic equation of the polynomial is,

p(x) = 3x² - 12x + k

(alpha - beta)² = (alpha + beta)²- 4alphabeta

where,

alpha+beta = -b/a = -(-12/3) = 4

alphabeta = c/a = k/3

by substituting the given values in the formula,

(2)² = 4² - 4(k/3)

4 - 16 = -4k/3

-12 = -4k/3

36 = 4k

thus, k = 9