Question

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

Answer 1

here is your answer, mate

Answer 2

A quadratic polynomial whose zeroes are $-\frac{1}{2}$ and $\frac{2}{3}$  is   $x^2-x-2=0$

Step-by-step explanation:

To find : A quadratic polynomial whose zeroes are $-\frac{1}{2}$ and $\frac{2}{3}$ ?

Solution :

The roots of the quadratic equation $ax^2+bx+c=0$ are $\alpha$  and $\beta$.

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

The formula to get the equation is

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

Substitute the values,

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

$x^2-\frac{1}{6}x-\frac{1}{3}=0$

$x^2-x-2=0$

Therefore, a quadratic polynomial whose zeroes are $-\frac{1}{2}$ and $\frac{2}{3}$  is   $x^2-x-2=0$

#Learn more

Write quadratic equation whose roots are  2 and 4.​

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