Question

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

Answer 1

Answer :

The value of ‘a’ is 3.

Explanation :

Given polynomial,

→ (a² + 9)x² + 13x + 6a

Comparing with general form of equation ax² + bx + c.

• a = (a² + 9)
• b = 13
• c = 6a

Assuming α as one zero,

A/q, other zero will be 1/α

We know that,

• Product of zeroes = c/a = 6a/(a² + 9)

∴ α × 1/α = 6a/(a² + 9)

→ 1 = 6a/(a² + 9)

→ a² + 9 = 6a

→ a² + 9 - 6a = 0

→ a² - 3a - 3a + 9 = 0

→ a(a - 3) - 3(a - 3) = 0

→ (a - 3)(a - 3) = 0

∴ a = 3