Quadratic Equations - Olympiad Level MCQ, Class 10 Mathematics - Class 10 MCQ

If α,β are the roots of the equation x² + 2x + 4 = 0, then  is equal to :

If    then :

If α, β are the roots of the equation x² + 7x + 12 = 0, then the equation whose roots are (α + β)² and (α – β)² is:

The value of k (k > 0) for which the equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots is :

If α,β are roots of the quadratic equation x² + bx – c = 0, then the equation whose roots are b and c is

Solve for y : 9y⁴ – 29y² + 20 = 0

Solve for x : x⁶ – 26x³ – 27 = 0

 If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is       

Solve :  –  = 3

Solve for x :   :

Solve x :  :

Solve for x :  – x + 2 =  , x ε R :

Solve for x : 3^x+2 + 3^-x = 10

Solve for x : (x + 1) (x + 2) (x + 3) (x + 4) = 24 (x ε R) :

The sum of all the real roots of the equation |x – 2|² + |x – 2| – 2 = 0 is :

If a, b ε {1, 2, 3, 4}, then the number of quadratic equations of the form ax² + bx + 1 = 0, having real roots is :

The number of real solutions of x –   is :

Ifthen x is equal to :

The quadratic equation 3x² + 2(a² + 1) x + a² – 3a + 2 = 0 possesses roots of opposite sign then a lies in:

The equation has :

The number of real solutions of the equation 2|x|² – 5|x| + 2 = 0 is :

The number of real roots of the equation (x – 1)² + (x – 2)² + (x – 3)² = 0 :