Question

If one zero of polynomial (a2+9)x2+13x+6a is reciprocal of another find a

Answer 1

Questions should be:

• If one zero of polynomial (a²+9)x²+13x+6a is reciprocal of another find a.

ANSWER:

• Value of a is 3

GIVEN:

• P(x) = (a²+9)x²+13x+6a
• One zero is reciprocal of other.

TO FIND:

• Value of 'a'.

SOLUTION:

Let one zero of the polynomial be 'x'.

Other zero = 1/x

Finding product of zeros (αβ)

= x*(1/x)

= 1

Formula:

=> Product of zeros (αβ) = Constant term/ Coefficient of x²

Here:

Constant term = 6a

Coefficient of x² = a²+9

Putting the values in the formula:

=> 1 = 6a/a²+9

=> a²+9 = 6a

=> a²-6a+9 = 0

=> (a)² -2(a)(3) + (3)² = 0

=> (a-3)² = 0

=> a-3 = 0

=> a = 3

Value of a is 3