Question

17)If one zero of the polynomial p(x)=(a²
+4 )x²

+13x+4a is the reciprocal of the other,find a.​

Answer 1

Step-by-step explanation:

p(x) = (a² + 4)x² + 13x + 4a

Let the zeroes of the polynomial be α and β.

Given, β = 1/α

Product of zeroes = c/a

$\alpha \times \beta = \frac{ 4a}{ {a}^{2} + 4} \\ \alpha \times \frac{1}{ \alpha } = \frac{4a}{ {a}^{2} + 4 } \\ 1 = \frac{4a}{ {a}^{2} + 4 } \\ {a}^{2} + 4 = 4a \\ {a}^{2} - 4a + 4 = 0 \\ {a}^{2} - 2a - 2a + 4 = 0 \\ (a - 2) (a - 2) = 0 \\ {(a - 2)}^{2} = 0 \\ a - 2 = 0 \\ a = 2$