Q14 of 113 Page 50

Find the quadratic polynomial whose zeros are . Verify the relation between the coefficients and the zeros of the polynomial.

Now, Sum of zeros,

And, product of zeroes,

We know that,

Required polynomial = x²–(α + β)x + αβ

=12x² – 5x – 2

Now, sum of zeroes

Product of zeroes

Hence, relationship verified.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

3x² – x – 4

Find the quadratic polynomial whose zeros are 2 and ‒6. Verify the relation between the coefficients and the zeros of the polynomial.

Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is ‒1. Hence, find the zeros of the polynomial.