Question

Find quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.5,-2 .​

Answer 1

Given: Sum of the zeroes is 5 and product of the zeroes is -2.

To find: A quadratic polynomial.

Answer:

The general form of a quadratic polynomial is:

$\sf \bf x^2 - (sum\ of\ the\ zeroes)x\ +\ (product\ of\ the\ zeroes)$

We know that the sum of the zeroes is 5 and product of the same is -2.

Substituting the values in the respective places,

$\sf x^2 - 5x - 2$

Answer 2

Let a and b be the zeros of the required polynomial

Implies,

a=5 and b= -2

Now,

★Sum of Zeros:

a + b

= 5+(-2)

=3

★Product of Zeros:

ab=5(-2) = -10

Required Polynomial:

x²-(a+b)x+ab

=x²-(3)x+(-10)

=x²-3x-10