The Expression ax2 + bx + c has The Same Sign As Of a if

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

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

The number of real roots of the equation (x + 3)⁴ + (x + 5)⁴ = 16 is

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

If the graph of the function y = 16x² + 8(a + 5) x – 7a – 5 is strictly above the x – axis, then ‘a’ must satisfy the inequality