Question

If sum of square of zeros of polynomial 3x2 + 5x + k is -2/3.
Find value of k

Answer 1

Let a and b be zeroes of the polynomial,

then (a+b) = -3/5

ab = k/5

Now,

a²+b² = 11/25

⇒(a+b)² - 2ab = 11/25

⇒(-3/5) -2(k/5) = 11/25

⇒9/25 - 2k/5 = 11/25

⇒2k/5 = 9/25 - 11/25 = -2/25

⇒k = -1/5