Question

For each of the following, find a quadratic polynomial whose sum and product
respectively of the zeroes are as given. Also find the zeroes of these polynomials
by factorisation.
(i)-3, 2

Answer 1

Answer:

Required quadratic polynomial:

x² + 3x + 2

Zeros : x = -1 , -2

Note:

• If A and B are the zeros of any quadratic polynomial , then it is given as ;

x² - (A+B)x + A•C

• The possible values of variable for which the polynomial becomes zero are called its zeros.

• To find the zeros of a polynomial , equate it to zero.

Solution:

Here,

The sum of zeros of required quadratic polynomial is -3.

Thus,

A + B = -3 ------(1)

Also ,

The product of zeros zeros of the required quadratic polynomial is 2 .

Thus,

A•B = 2 --------(2)

Thus,

The required quadratic polynomial will be;

=> x² - (A+B)x + A•B

=> x² - (-3)x + 2

=> x² + 3x + 2

Now,

In order to find the zeros of obtained quadratic polynomial , equate it to zero.

Thus,

=> x² + 3x + 2 = 0

=> x² + x + 2x + 2 = 0

=> x(x + 1) + 2(x + 1) = 0

=> (x+1)(x+2) = 0

=> x = -1 , -2