Question

quadratic polynomial with the sum and product of its zeroes are 2 and 1/ 2. is​

Answer 1

The general formula for a quadratic polynomial is given by :

P(x) = k[ x² - (sum of zeroes) x + product of zeroes]

Given that sum of zeroes = 2

Product of zeroes = $\dfrac{1}{2}$

Hence ,

$\sf \: p(x) = k ( {x}^{2} - 2 + \frac{1}{2} )$

Taking the LCM

$\sf \implies \: p(x) = k(\frac{2 {x}^{2} - 4 + 1 }{2} )$

Let p(x) = 0

$\implies \: \therefore \sf 0 \times 2 = k(2 {x}^{2} - 4x + 1)$

$\implies \sf \: 0 = k(2 {x}^{2} - 4x + 1)$

So , our required quadratic polynomial with sum of zeroes and product of zeroes as 2 and $\frac{1}{2}$ is :

$\boxed{\large \rm \purple{p(x ) = k(2 {x}^{2} - 4x + 1)}}$

Where K is any constant value .