Question

16 If one zero of the polynomial for (a^2+4)x^2+9x+4a is
the reciprocal of the other, find the value of a​

Answer 1

Answer:

$a = 2$

Step-by-step explanation:

GIVEN

⇒ The given quadratic polynomial is

$( {a}^{2} + 4) {x}^{2} + 9x + 4a$

⇒ One of the zeros of the polynomial is reciprocal of the other

$\beta = \frac{1}{ \alpha }$

$or \: \alpha \beta = 1$

CALCULATION

We know that

$\alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$1 = \frac{4a}{ {a}^{2} + 4}$

${a}^{2} + 4 = 4a$

${a}^{2} - 4a + 4 = 0$

${(a - 2)}^{2} = 0$

$a = 2$

Answer 2

Answer:

hint let  α and 1/α are the zeroes of the given polynomial

α x 1/α = 4a/a^2 + 4 ⇒1 = 4a/a^2 + 4

a^2 + 4 = 4a ⇒ (a - 2 )^2 = 0

ans  a = 2

from all in one class 10 21-22