Question

If one zero of the polynomial (a^2+2)x^2 +10x +3a is the reciprocal of the other. find a

Answer 1

Let one zero be α
Then other zero=1/α

product of zeroes=c/a

$\alpha \times \frac{1}{ \alpha } = \frac{c}{a} \\ \\ 1 = \frac{3a}{ {a}^{2} + 2} \\ \\ {a}^{2} + 2 = 3a \\ \\ {a}^{2} - 3a + 2 = 0 \\ \\ {a}^{2} - a - 2a + 2 = 0 \\ \\ a(a - 1) - 2(a - 1) = 0 \\ \\ (a - 1)(a - 2) = 0 \\ \\ a - 1 = 0 \\ a = 1 \\ \\ a - 2 = 0 \\ a = 2$