Question

5.If one root of the polynomial f(x)=5x²+13x+k is reciprocal of the other, then the value of k is:

Answer 1

EXPLANATION.

• GIVEN

one roots of the polynomial f(x) = 5x² + 13x + k

is reciprocal of the other

To find value of k.

According to the question,

=> equation = f(x) = 5x² + 13x + k

products of zeroes of quadratic equation.

=> ab = c/a = k/5

one roots is reciprocal to each other.

=> a X 1/a = 1

=> 1 = k/5

=> k = 5

Therefore,

value of k = 5

Answer 2

Given :-

• One root of the polynomial f(x) = 5x²+13x+k is reciprocal of the other.

To Find :-

• Value of k.

Solution :-

Equation,

$\sf f(x) = {5x}^{2} + 13x + k$

Product of zeros on quadratic equation,

$\implies \sf ab = \frac{c}{a} = \frac{k}{5}$

One root is reciprocal to each other,

$\implies \sf a \times \frac{1}{a} = 1$

$\implies \sf1 = \frac{k}{5}$

$\implies \sf k = 5$

Answer :-

• Value of k = 5