Question

if one zero of the polynomial (a^2 +9)x^2+13x+6a is the reciprocal of the other. find the value of a
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Answer 1

Answer:

a = 3

Step-by-step explanation:

1). (a ± b)² = a² ± 2ab + b²

2). If  α and β are zeroes of ax² + bx + c , then αβ = c/a

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Let α and β be zeroes of the polynomial (a² + 9)x² + 13x + 6a , then

αβ = $\frac{6a}{a^2+9}$ = 1 ⇒ a² + 9 = 6a

a² - 6a + 9 = 0 ⇔ (a - 3)² = 0 ⇒ a = 3