Question

Find a quadratic polynomial whose zeroes are 3 and 2

Answer 1

hi friend,

given.,a quadratic polynomial whose zeroes are 3 and 2

<>sum of zeros →3 + 2→5

<>product of zeros → (3)(2)=6

quadratic polynomial will be

<>x²-(sum of zeros)x+product of zeros 

<>x²-5x+6

I hope this will help u:)

Answer 2

The quadratic polynomial whose zeroes are 3 and 2 is given as $x^{2} -5x+6 =0$

Step-by-step Explanation

Given:

The zeroes of a quadratic polynomial are 3 and 2.

To be found:

To find the quadratic polynomial using the given zeroes of the polynomial.

Formula Used:

If $\alpha$ and $\beta$ are the zeroes of a quadratic polynomial, then the formula to find the quadratic polynomial is given as,

$x^{2} -(\alpha +\beta )x+\alpha \beta =0$       -----------(1)

Solution:

Here, the zeroes or roots of the quadratic polynomial are given as 2 and 3.

$\implies \alpha =2$ and $\beta =3$

So, the sum of the zeroes of the polynomial, $\alpha +\beta =2+3=5$  --------(2)

Also, the products of the zeroes of the polynomial, $\alpha \beta =(2)(3)=6$  --------(3)

Now, substituting (2) and (3) in (1), we get

$x^{2} -5x+6 =0$

Therefore, $x^{2} -5x+6 =0$ is the required quadratic polynomial.

#SPJ2