if a and b are the zeros of kx2+4x+4 such that a2 +b2 =24,find the value of k - Maths - Polynomials

Question

if a and b are the zeros of kx2+4x+4 such that a2 +b2 =24,find
the value of k

Chetna Khanna · Accepted Answer

Given polynomial is kx2 + 4x + 4 whose zeros are a and b Sum of zeros, a + b = $- \frac{4}{k}$ Product of zeros, ab = $\frac{4}{k}$ $(a + b)^{2} = a^{2} + b^{2} + 2 a b \Rightarrow {(- \frac{4}{k})}^{2} = 24 + 2 (\frac{4}{k}) \Rightarrow \frac{16}{k^{2}} = 24 + \frac{8}{k} \Rightarrow 24 k^{2} + 8 k - 16 = 0 \Rightarrow 3 k^{2} + k - 2 = 0 \Rightarrow 3 k^{2} + 3 k - 2 k - 2 = 0 \Rightarrow 3 k (k + 1) - 2 (k + 1) = 0 \Rightarrow (k + 1) (3 k - 2) = 0 \Rightarrow k = - 1 o r k = \frac{2}{3}$