Question

Find the zeroes of the polynomial q(x) = 8x² – 2x – 3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).

Find the zeroes of the polynomial r(x) = 4x² + 3x − 1. Hence, write a polynomial whose zeroes are reciprocal of the zeroes of polynomial r(x).

The sides of a right triangle are such that the longest side is 4 m more than the shortest side and the third side is 2 m less than the longest side. Find the length of each side of the triangle. Also, find the difference between the numerical values of the area and the perimeter of the given triangle.

Express the equation (x – 2)/(x – 3) + (x – 4)/(x – 5) = 10/3 ; (x ≠ 3, 5) as a quadratic equation in standard form. Hence, find the roots of the equation so formed.