Question

If one zero is (a⁴+4)x+13x+4x is reciprocal of other.Find a

Answer 1

Answer;

Correct Question: (a² + 4)x² + 13x + 4a

Given that-

One zero is reciprocal to other.

Product of zeroes = c/a

⇒ α * 1/α = 4a /a² + 4

⇒ 1 = 4a/a² + 4

⇒ a² + 4 = 4a

⇒ a² + 4a + 4 = 0

⇒ a² + 2a + 2a + 4 = 0

⇒ a (a + 2) + 2 (a + 2) = 0

⇒ (a + 2)(a + 2) = 0

∴ a = - 2 or a = - 2

Hence, the value of a is -2.