1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.Solutions:(i) x2–2x –8

To find the zeroes of the quadratic polynomial x² - 2x - 8, we first need to write the polynomial in the standard form ax² + bx + c = 0. In this case, a = 1, b = -2, and c = -8.

The formula to find the zeroes of a quadratic polynomial is given by:

x = [-b ± sqrt(b² - 4ac)] / 2a

Substituting the values of a, b, and c in the formula, we get:

x = [2 ± sqrt((-2)² - 41(-8))] / 2*1 x = [2 ± sqrt(4 + 32)] / 2 x = [2 ± sqrt(36)] / 2 x = [2 ± 6] / 2

So, the zeroes of the polynomial are x = 4 and x = -2.

Now, let's verify the relationship between the zeroes and the coefficients. According to the relationship, the sum of the zeroes is -b/a and the product of the zeroes is c/a.

Sum of the zeroes = 4 + (-2) = 2 -b/a = -(-2)/1 = 2

Product of the zeroes = 4 * -2 = -8 c/a = -8/1 = -8

Since the sum and product of the zeroes are equal to -b/a and c/a respectively, the relationship between the zeroes and the coefficients is verified.