Quadratic Equation Questions

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is :

The number of points in (- ∞,∞), for which x2 - xsinx - cosx = 0, is

Let α and β be the roots of equation px2 + qx + r = 0, p ≠ 0. If p, q, r are in A.P. and , then the value of |α - β| is...

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

If α, β∈C are the distinct roots of the equation x2 - x + 1 = 0, thenα101 +β107 is equal to-...

Let g(x) = cos x2, f(x) = x and α, β (α<β) be the roots of the quadratic equation 18x2 - 9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y =...

Let a ∈ R and let f : R → R be given by f(x) = x5 - 5x + a. Then

Let S be the set of all non-zero numbers a such that the quadratic equation αx2 − x + a = 0 has two distinct real roots x1 and x2 satisfying the inequality |x1 − x2| < 1. Which of ...

The number of values of k, for which the system of equations :(k + 1)x + 8y = 4kkx + (k + 3)y = 3k - 1has no solution, is :

The equation esinx - e-sinx - 4 = 0 has :

Let (x0, y0) be solution of the following equations (2x)ln2 = (3y)ln3 3lnx = 2lny Then x0 is...

Let α and β be the roots of x2 - 6x - 2 = 0,, with α > β. If an = αn - βn for n ≥ 1. then the value of is...

A value of b for which the equations x2 + bx - 1 = 0 x2 + x + b = 0,have one root in common is...

Let α (a) and β (a) be the roots of the equation where a > - 1. Then α(a) and β(a) are...

If α and β are the roots of the equation x2 - x + 1 = 0, then α2009 + β2009 =

Let p and q be real numbers such that p ≠ 0, P3 ≠ -q. If α and β are nonzero complex numbers satisfying α + β = - p and α3 + β3 = q. then a quadratic equation...

Let a > 0, b > 0 and c > 0. Then, both the roots of the equation ax2 + bx + c = 0.

Both the roots of the equation (x - b)(x - c) + (x - a)(x - c) + (x - a)(x - b) = 0 are always

The least value of the experssion 2 log10 x - logx (0.01),for x > 1, is...

The number of real solutions of the equation |x|2 - 3|x| + 2 = 0 is