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If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 + bx + 1 = 0 having real roots is A. 10 B. 7 C. 6 D. 12 |
Answer» For quadratic equation to have real roots, d≥ 0 b2 – 4a ≥ 0 b2 ≥ 4a For a = 1, 4a = 4, b = 2, 3, 4 (3 equations) With values of (a,b) as (1,2), (1,3), (1,4) a = 2, 4a = 8, b = 3, 4 (2 equations) With values of a,b as (2,3), (2,4) a = 3, 4a = 12, b = 4 (1 equation) With value of (a,b) as (3,4) a = 4, 4a = 16, b = 4 (1 equation) With values of (a,b) as (4,16) Thus, total 7 equations are possible. |
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