Quadratic Equation Questions

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 =...

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

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 ...

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...

If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is

The quadratic equations x2 - 6x + a = 0 and x2 - cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is...

If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is

If the roots of the quadratic equation x2 + px + q = 0 are tan30o and tan15o, respectively then the value of 2 + q - p is

All the values of m for which both roots of the equations x2 - 2mx + m2 - 1 = 0 are greater than -2 but less than 4, lie in the interval

The value of α for which the sum of the squares of the roots of the equation x2 - (a - 2)x - a - 1 = 0 assume the least value is

If roots of the equation x2 - bx + c = 0 be two consectutive integers, then b2 - 4c equals

Let α and β be the distinct roots of ax2 + bx + c = 0, then isequal to

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation