Question

If one zero of the polynomial p(x) = (a2 +9)x2 + 45x + 6a is the reciprocal of the other, find the value of ‘a’

Answer 1

I hope you understood

Answer 2

Answer:

Value of a is 3.

Step-by-step explanation:

Given Polynomial, p(x) = ( a² + 9 ) x² + 45x + 6a

One zero is reciprocal of another zero

Let say α be one zero

⇒ $\frac{1}{\alpha}$ is 2nd zero.

According relation of coefficient and zeroes, we have

$Product\:of\:zeroes=\frac{c}{a}$

$\alpha\times\frac{1}{\alpha}=\frac{6a}{a^2+9}$

$a^2+9=6a$

$a^2-6a+9=0$

$a^2-3a-3a+9=0$

$a(a-3)-3(a-3)=0$

$(a-3)(a-3)=0$

⇒ a - 3 = 0 ⇒ a = 3

Therefore, Value of a is 3.