Question

Find k , if one zero of the polynomial kx^2 - x + ( 1/3 ) is reciprocal of the other.​

Answer 1

Answer:

$\frac{1}{3}$

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

GIVEN

one zero of the polynomial $\displaystyle \: \: k {x}^{2} - x + \frac{1}{3}$ is reciprocal of the other.

CALCULATION

The given Quadratic polynomial is $\displaystyle \: \: k {x}^{2} - x + \frac{1}{3}$

Comparing with $a {x}^{2} + bx + c$

We get$a = k , b = - 1 , c = </strong><strong>\frac{1}{3}$

Let $\alpha \: \: and \: \: \beta \:$are the zeroes of the given quadratic polynomial

So

$\beta = \frac{1}{ \alpha }$

So

$\alpha \beta =1$

$\implies \displaystyle \: \: \frac{1}{3k} = 1$

$\implies \displaystyle \: \: {3k} = 1$

$\implies \displaystyle \: k = \frac{1}{3}$