For what value of k, x = a is a solution of the equation

x² – (a + b) x + k = 0.

For what value of k, is a solution of the equation 3x² + 2kx — 3 = 0

For what values of a and b, and x = — 2 are solutions of the equation ax² + bx — 6 = 0.

Determine the value of k, a and b in each of the following quadratic equation, for which the given value of x is the root of the given quadratic equation:

(i) kx² — 5x + 6 = 0 ; x = 2

(ii) 6x² + kx — √6 = 0;

(iii) ax² — 13x + b = 0; x =2 and x = —2 find a, b

(iv) ax²+ bx – 10 = 0; and

Find the roots of the following quadratic equations by factorisation:

2x² — 5x + 3 = 0