Question

if one root of 9x^2+13x+6a is a reciprocal of the other then a is equal to​

Answer 1

Answer:

a=3/2

Step-by-step explanation:

In the quadratic equation $ax^2+bx+c=0$,

multiplication of its two roots is equal to $\frac{c}{a}$.

The question said one root is a reciprocal of other.

Therefore, $\frac{c}{a}=1$. According to the question, a=9, c=6a.

$\frac{6a}{9} =1$

$6a=9$

$2a=3$

Therefore a=3/2.

Answer 2

Answer:

a=3/2

Step-by-step explanation:

In the quadratic equation ax^2+bx+c=0ax2+bx+c=0 ,

multiplication of its two roots is equal to \ frac{c}{a}ac .

The question said one root is a reciprocal of other.

Therefore, \ frac{c}{a}=1ac=1 . According to the question, a=9, c=6a.

\ frac{6a}{9} =196a=1

6a=96a=9

2a=32a=3

Therefore

a=3/2.