Q. 133.8( 5 Votes )

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

Answer :

(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


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