Question

If zeroes of the polynomial x^2+Ax-b are reciprocal of each other ,then b is

Answer 1

Answer:

it means product of zeros is 1

-b=1

b= -1

Answer 2

Given,

• A polynomial $x^{2} + Ax - b$

• Its roots are reciprocal of each other.

To find,

The value of b.

Solution,

The given polynomial is a quadratic equation.

For a quadratic equation of the general form, the relationship between the roots of the equation and the coefficients are as follows:-

Sum of roots $( \alpha + \beta ) = \frac{-b}{a}$

Product of roots $( \alpha\beta ) = \frac{c}{a}$

Comparing the given equation we have,

• a = 1

• b = A

• c = -b

If one of the roots of the equation is $\alpha.$ The other root will be $\frac{1}{\alpha }$.

Product of roots = $\alpha*\frac{1}{\alpha } = 1 = \frac{-b}{1}$

                        $b = -1$

Therefore, the value of b is -1.