The roots of the equation $$3x^2+ 5x-a = 0$$​ are the reciprocals of each other. What is the value of a?

Correct option is B

Given:

​$$3x^2 + 5x - a = 0$$ 

Roots of the equation are reciprocals 

Concept Used:

If the roots of the quadratic equation$$Ax^2 + Bx + C = 0$$​ are $$r_1$$ and $$r_2$$​ . Then 

the sum of the roots is given by: $$r_1+r_2= - \frac{B}{A}$$ 

And The product of the roots is given by: $$r_1 \cdot r_2 = \frac{C}{A}$$ 

Solution:

We are given the quadratic equation: 

​$$3x^2 + 5x - a = 0$$ 

​Let the roots of the quadratic equation be $$r_1$$​and $$r_2$$ According to the problem, these roots are reciprocals, so:

​$$r_1= \frac{1}{r_2}$$ 

​For the equation $$3x^2 + 5x - a = 0$$ , 

The sum of the roots is: 

​$$r_1+r_2= - \frac{B}{A}$$  =  $$\frac{5}{3}$$ 

The product of the roots is:

​$$r_1 \times r_2 = \frac{C}{A} = \frac{-a}{3}$$ 

Since the roots are reciprocals, we have $$r_1= \frac{1}{r_2}$$​, so the product of the roots is:

​$$r_1 \times r_2 = 1$$ 

$$\frac{-a}{3}= 1$$ 

−a =3  =>  a  = −3 

Thus the value of $a$ is -3 .−3\boxed{-3}
​

​