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 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

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

The expression ax² + bx + c has the same sign as of a if