Question

if one zero of the polynomial (a^2+9)x^2+13 x +6 is reciprocal of the other, find the value of a​

Answer 1

Answer:

Value of a is ± √3 i

Step-by-step explanation:

Let the zeroes of the polynomial be y, 1/y

Comparing the given polynomial with Ax² + Bx + C we get

• A = a² + 9
• B = 13
• C = 6

Product of zeroes = C/A

y × 1/y = 6/(a² + 9)

1 = 6/(a² + 9)

a² + 9 = 6

a² = 6 - 9

a² = - 3

a = ± √( - 3 ) = ± √3 i

Therefore the value of a is ± √3 i