## If ax^2 + bx + 6 = 0 does not have two distinct real roots where…

Q : If ax2 + bx + 6 = 0 does not have two distinct real roots where a, b ∈ R, then the least value of 3a + b is (A) 4 (B) -1 (C) 1 (D) -2 Ans: (D) Sol. D ≤ 0 ⇒ f(x) ≥ 0 or, f(x) ≤ 0 for all … Read more

## The values of α and β such that equation x^2 + 2x + 2 + e^α – sinβ = 0 have a real solution is

Q : The values of α and β such that equation x2 + 2x + 2 + eα – sinβ = 0 have a real solution is (A) $\large \alpha , \beta \in R$ (B) $\large \alpha \in (0 , 1) \; , \beta \in (\pi/2 , 2 \pi)$ (C) \$\large \alpha \in … Read more

## The quadratic equation whose roots are A.M. and H.M. between the roots of the equation…

Q : The quadratic equation whose roots are A.M. and H.M. between the roots of the equation ax2 + bx + c = 0 is (A) abx2 + (b2 + ac)x + bc = 0 (B) 2abx2 + (b2 + 4ac)x + 2bc = 0 (C) 2abx2 + (b2 + ac)x + bc = 0 … Read more