Question

The sum and product of the zeros of a quadratic polynomial are $-\frac{1}{2} and -3$ respectively. What is the quadratic polynomial.

Answer 1

SOLUTION :

Let α and β are the zeroes of the quadratic polynomial

Given :  α + β = -1/2 ………… (1)  

αβ = -3 ………………..(2)

Then, the quadratic polynomial is :  

k[x² –(sum of the zeroes)x + (product of the zeroes)]

k[x² –(α + β)x + (α β)]

=k[ x² + ½ x + (-3)]

[From eq 1 & 2]

= k[ x² + x/2 -3]

[K is any non zero real number]

Hence, the required quadratic polynomial is f(x) =k (x² + x/2 -3)

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

Step-by-step explanation:

X^2-(sum of zero)x+product of zero

X^2-(1/2)x+(-3)

2x^2-x-3