Question

if one zero of the polynomial p(x)=(a²+9)x²+45x +6a is the recipeocal of the other , then the value of a is?​

Answer 1

3

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}

α

1

is 2nd zero.

According relation of coefficient and zeroes, we have

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

a

c

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

α

1

=

a

2

+9

6a

a^2+9=6aa

2

+9=6a

a^2-6a+9=0a

2

−6a+9=0

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

2

−3a−3a+9=0

a(a-3)-3(a-3)=0a(a−3)−3(a−3)=0

(a-3)(a-3)=0(a−3)(a−3)=0

⇒ a - 3 = 0 ⇒ a = 3

Therefore, Value of a is 3.

Answer 2

$\huge \underline \bold \pink{Solution : }$

Given that :

Polynomial = (a²+9)x²+45x +6a

Where a = (a²+9), b = 45 and c = 6a

Let, the one zero of the given polynomial be y then other will be 1/y

As we know that :

Product of Zeroes = c/a

=> y × 1/y = 6a/(a²+9)

=> 6a/(a²+9) = 1

=> 6a = (a²+9)

=> a² + 9 - 6a = 0

=> a² - 6a + 9 = 0

=> (a - 3)² = 0

=> a = 3

Therefore, the value of a will be 3 ✔✔

$\huge \fbox \green{Hope it helps ☺}$