Question

The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $-2$ is:

• A. $x^2+3x-2=0$
• B. $x^2-2x+3=0$
• C. $x^2-3x+2=0$
• D. $x^2-3x-2=0$

Answer 1

Answer: (D)

Given: sum of zeroes is $3$ and product of zeroes is $-2$

Let the zeroes of the polynomial be $\alpha ,\beta$

According to the question,

$\alpha +\beta =3,\alpha \beta =-2$

We know, $\alpha +\beta =-\frac{b}{a}=3⟹b=-3a$ ....... $\left(i\right)$

And, $\alpha \beta =\frac{c}{a}=-2⟹c=-2a$ ....... $\left(ii\right)$

Now, the general form of quadratic equation is:

$a{x}^2+bx+c=0$

From equation $\left(i\right)$ and $\left(ii\right),$ we get

$a{x}^2+(-3a)x+(-2a)=0⟹a(x^2-3x-2)=0$

Hence, the required polynomial is $x^2-3x-2=0$