InterviewSolution
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InterviewSolution
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Which of the following equations has two distinct real roots?(a) 2x2-3√2x + 9/4 =0(b) x2 + x – 5 =0(c) x2 + 3x + 2√2 =0(d) 5x2- 3x + 1=0 |
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Answer» (b) x2 + x – 5 = 0 Same as the previous one. Let’s check the discriminant value for distinct real roots. a. Given, 2x2 - 3√2x + 9/4 = 0 ∴ D = b2 - 4ac = 0 = (-3√2)2 - 4(2) (9/4) = 18 - 18 = 0 Hence, the roots are real and equal. b. Given, x2 + x – 5 = 0 ∴ D = b2 - 4ac = 0 = (1)2 - 4(1) (-5) = 1 + 20 = 21 > 0 Hence, the roots are real and distinct. c. Given, x2 + 3x + 2√2 =0 ∴ D = b2 - 4ac = 0 = 32 - 4(1) (2√2) = 9 - 8√2 < 0 Hence, the roots are imaginary. d. Given, 5x2 - 3x + 1 = 0 ∴ D = b2 - 4ac = 0 = (-3)2 - 4(5)(1) = 9 – 20 < 0 Hence, the roots are imaginary. |
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