Question

1. Write a quadratic equation, whose sum and product of zeroes is -5 and 2

respectively.
​

Answer 1

Step-by-step explanation:

Given,

Sum of zeroes= -5

Product of zeroes= 2

x²+(sum of zeroes)x+(product of zeroes)

=x²+(-5)x+(2)

=x²-5x+2

I hope it's help you

Answer 2

The quadratic equation, whose sum and product of zeroes are -5 and 2 respectively, is $x^{2} +5x+2=0$.

Given,

For a quadratic equation,

sum of zeroes = -5,

product of zeroes = 2.

To find,

The quadratic equation.

Solution,

For a quadratic equation

$ax^{2} +bx+c=0$     ...(1)

if $\alpha \hspace{3} and \hspace{3} \beta$ are the roots or zeroes, then their sum and product are given as,

the sum of zeroes, $\alpha +\beta =-\frac{b}{a}$

product of zeroes, $\alpha \beta =\frac{c}{a}$

Or, we can also say,

$\frac{b}{a}=-(\alpha +\beta )$, and,

$\frac{c}{a}=\alpha \beta$

Now, if we divide the eq. (1) by $a$, we get,

$x^{2} +\frac{b}{a} x+\frac{c}{a} =0$     ...(2)

Using the above equation (2), we can find a quadratic equation when the sum and product of zeroes are known.

Here, it is given that,

$\alpha +\beta =-5$

$\alpha \beta=2$

So,

$\frac{b}{a}=-(\alpha +\beta ) =-(-5)=5$

$\implies \frac{b}{a}=5$

and,

$\frac{c}{a} =\alpha \beta =2$

$\implies \frac{c}{a} =2$

Substituting these values in equation (2), we get,

$x^{2} +(5)x+(2)=0$

$\implies x^{2} +5x+2=0$, which is the required quadratic equation.

Therefore, the quadratic equation, whose sum and product of zeroes are -5 and 2 respectively, is $x^{2} +5x+2=0$.