Question

Determine k such that the quadratic equation
x^2 +7(3 + 2k) - 2x (1 + 3k) = 0 has equal roots :
(1) 2,7
(2) 7,5
(3) 2,-10/9
(4) None of these
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Answer 1

Answer:

The equation is x2 – x(2) (1 + 3k) + 7 (3 + 2&) = 0 The roots are real and equal ⇒ ∆ = 0 (i.e.,) b2 – 4ac = 0 Here a = 1, b = -2 (1 + 3k), c = 7(3 + 2k) So b2 – 4ac = 0 ⇒ [-2 (1 + 3k)]2 – 4(1) (7) (3 + 2k) = 0 (i.e.,) 4 (1 + 3k)2 – 28 (3 + 2k) = 0 (÷ by 4) (1 + 3k)2 – 7(3 + 2k) = 0 1 + 9k2 + 6k – 21 – 14k = 0 9k2 – 8k – 20 = 0 (k – 2)(9k + 10) = 0 k - 2 = 0 or 9k + 10 = 0 k = 2 or k = -10/9 To solve the quadratic inequalities ax2 + bx + c < 0 (or) ax2 + bx + c > 0Read more on Sarthaks.com - https://www.sarthaks.com/907036/find-the-values-of-k-so-that-the-equation-x-2-2x-1-3k-7-3-2k-0-has-real-and-equal-roots