Question

1/4,-1 ..find a quadratic polynomial each with given numbers as the sum and product of its zeroes respectively

Answer 1

given,sum of zero
$\alpha + \beta$1/4
product of zero alpha x beta=-1
therefore,the quadratic polynomial

x2-(alpha + beta)x + alpha x beta

Answer 2

The quadratic equation having the given sum and product of its zeros is 4x² -x -4 = 0.

Given,

Two numbers: 1/4 and -1.

To find,

A quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

Solution,

Firstly, let's consider a quadratic equation, which is

$ax^{2} +bx+c=0 \hfill ...(1)$

For any quadratic equation, the sum and product of its zeros are given by

$sum \hspace{3} of \hspace{3} zeros =-\frac{b}{a} \hfill ...(2)$

$product \hspace{3} of \hspace{3} zeros =\frac{c}{a} \hfill ...(3)$

So, we can write (1) as,

$x^{2} - (sum \hspace{3} of \hspace{3} zeros)x+ (product \hspace{3} of \hspace{3} zeros)=0 \hfill ...(4)$

It is given here that,

the sum of zeros = $\frac{1}{4}$, and

product of zeros = -1.

Substituting in (4), we can find the required equation as follows.

$x^{2} - (\frac{1}{4} )x+ (-1)=0$

Simplifying,

$4x^{2} -x-4=0$

which is the required equation.

Therefore, the quadratic equation having the given sum and product of its zeros is 4x² -x -4 = 0.

#SPJ3