Question

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

Answer 1

Heya!!

This quadratic polynomial has two roots let those two roots be p and q

FOR A GENERAL QUADRATIC POLYNOMIAL SAY F(x) = ax² + bx + c

product of it's roots ( p × q ) = c/a

=>

( a² + 9 ) x² + 13x + 6a

( p × q ) = 6a/ ( a² + 9 ) ... Equation ( i )

ACCORDING TO THE GIVEN QUESTION

p = 1/q

put value of p in Equation i we have

6a/ ( a² + 9 ) = 1

a² + 9 = 6a

a² - 6a + 9 = 0

a² -3a -3a + 9 = 0

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

( a - 3 ) = 0

a = 3

Answer 2

Step-by-step explanation:

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