Question

Find a quadratic polynomial, the sum and product of whose zeroes are respectively :

$5and-50$

• A. $x^2-5x-50$
• B. $x^2-x-50$
• C. $x^2-x-30$
• D. $x^2-x+50$

Answer 1

The correct option is A $x^2-5x-50$

Let the quadratic polynomial be $a{x}^2+bx+c$ and its zeros be $\alpha$ , $\beta$

We know that,

$\alpha +\beta =\frac{-b}{a}=\frac{-5}{1}$

$\alpha \times \beta =\frac{c}{a}=\frac{-50}{1}$

If, $a=1$, $b=-5$, $c=50$

Therefore,

The quadratic equation which fits the condition is $x^2-5x-50$