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

(i) kx² – 5x + 6 = 0

Put x = 2

(ii) k² – 5(2) + 6 = 0

4k – 10 + 6 = 0

4k = 4

k = 1

(iii) 6x² + kx — = 0

Put x = – 2/√3

0

18 – 2√3 k – 4√6 = 0

18 – 4√6 = 2√3k

3√3 – 2√2 = k

(iv) ax² + bx – 10 = 0

Put

4a – 10b – 250 = 0

4a – 10b = 250 (1)

Put x = 3/5

ax² + bx – 10 = 0

25a + 15b – 90 = 0 (divide by 5)

5a + 3b = 18 (2)

Eliminate (1) and (2)

4a – 10b = 250 ×5

5a + 3b = 18 ×4

b = –19

Put b = –19 in (1)

4a – 10b = 250

4a – 10(–19) = 250

4a + 190 = 250

4a = 60

a = 15