Question

if one root of the polynomial f (x) =​

Answer 1

Answer:

So, the correct answer is “Option B”.

Step-by-step explanation:

An algebraic equation with two as the degree is known as the Quadratic equation. Here, we have been given the equation f(x)=5x2+13x+k which has two as the degree and so the given equation is a quadratic equation. The standard quadratic equation is f(x)=ax2+bx+c with the roots α and β.

Let one of the roots of the given quadratic equation f(x)=5x2+13x+k be ‘a’ then, according to the question, the second root of the given quadratic equation f(x)=5x2+13x+k will be ‘1/a’.

Now, comparing the given f(x)=5x2+13x+k equation with the standard quadratic equation f(x)=ax2+bx+c to determine the values of a, b and c.

5x2+13x+k=ax2+bx+c⇒a=5⇒b=13⇒c=k

Now, the product of the roots is given as the ratio of the constant term and the coefficient of x2.

Substituting α=a,β=1a,c=k and a=5 in the formula α×β=ca to determine the value of k.

α×β=caa×1a=k5k=5×1=5

Hence, the value of ‘k’ in the equation f(x)=5x2+13x+k is 5 such that the roots are reciprocal to one another.