Question

If one of the zero of the polynomial p(x)= kx²+2x+5 is reciprocal of the other then find the value of k

Answer 1

Question:

If one of the zero of the polynomial p(x)= kx²+2x+5 is reciprocal of the other then find the value of k.

To find:

$\star To \: find \: the \: value \: of \: k$

Answer:

$The \: value \: of \: k \: is \: \underline{ \: \sf \red{\bold{5}} \: }$

Given:

★ p(x) = kx² + 2x + 5

★ Second zero of polynomial is reciprocal of first zero of polynomial.

Step-by-step explanation:

Let one zero of polynomial be x

$Let \: the \: other \: zero \: be \: \underline{\bold{\frac{1}{x} }}$

$k {x}^{2} + 2x + 5$

$Here, \: a = k, \: b = 2, \: c = 5$

We know that,

$\boxed{Product \: of \: roots = \frac{c}{a} }$

$\implies x \times \frac{1}{x} = \frac{5}{k}$

$\implies \not{x} \times \frac{1}{ \not{x}} = \frac{5}{k}$

$\implies 1 = \frac{k}{5}$

$\implies \underline{ \: \boxed{k = 5} \: }$

$\therefore The \: value \: of \: k \: is \: \underline{ \: \sf \pink{\bold{5}} \: }$

Hint given in the question:

Second zero of polynomial is reciprocal of first zero of polynomial.

⚠️Note⚠️

Read the hint properly.

More information:

$\bigstar Sum \: of \: roots = \frac{ - b}{a}$

$\bigstar Product \: of \: roots = \frac{c}{a}$