Question

Form a quadratic polynomial whose zeroes are 2/3 and -1/3

Answer 1

Answer:

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Step-by-step explanation:

Ur answer is given in the attachment above....

Answer 2

We need to recall the following rule for the quadratic equation.

• If $\alpha$ , $\beta$ are the roots of a quadratic equation, then the quadratic equation is,

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

This problem is about the roots of a quadratic equation.

Given:

$\frac{2}{3}$  and  $\frac{-1}{3}$  are the roots of the quadratic equation.

Let's consider,

  $\alpha =\frac{2}{3}$  and  $\beta =\frac{-1}{3}$

Then,

$\alpha +\beta =\frac{2}{3} +\frac{-1}{3} =\frac{1}{3}$

$\alpha \beta =\frac{2}{3} *\frac{-1}{3} =\frac{-2}{9}$

So, the required quadratic equation is

$x^{2} -(\frac{1}{3} )x+\frac{-2}{9} =0$

$x^{2} -(\frac{1}{3} )x-\frac{2}{9} =0$

$9x^{2} -3x-2 =0$

Thus, the quadratic equation is $9x^{2} -3x-2 =0$.