If 1 Lies Between The Roots Of The Equation 3x2 – 3 Sin α x – 2 Cos2 α = 0 Then α Lies In The Interval

Let α, β be the roots of x² – x + p = 0 and γ, δ be the roots of x² – 4x + q = 0. If α, β, γ, δ are in G.P., then the integral values of p and qrespectively, are

Let P, Q, R be defined as

       P = a²b + ab² – a²c – ac²,

       Q = b²c + bc² – a²b – ac²

       R = a²c + c²a – c²b – cb²

Where a, b, c are all + ive and the equation Px² + Qx + R = 0 has equal roots then a, b, c are in

Let α and β are the roots of equation x² + x + 1 = 0. The equation whose roots are α¹⁹, β⁷ is

If x² + x + 1 is a factor ax³ + bx² + cx + d, then the real root of ax³ + bx²+ cx + d = 0 is

If one root of the equation (a² – 5a + 3)x² + (3a – 1)x + 2 = 0 be double the other, then the value of α is:

For the equation 3x² + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

If the roots of the equation x² – 2ax + a² + a – 3 = 0 are real and less than 3, then

If b > a, then the equation (x – a) (x – b) – 1 = 0, has

If α and β (α < β), are the roots of the equation x² + bx + c = 0, where c < 0 < b, then

Let α,β be the roots of the equation x² – px + r = 0 and  2β be the roots of the equation x² – qx + r = 0. Then the value of r is