Question

For real x, the expression [(x + m)2 – 4mn]/[2(x – n)] can be have any value except

Solution

Correct option is

Between 2m and 2 n

Δ = (y – 2m) (y – 2n) is + ive

 ∴ y shall not lie between 2m and 2n

SIMILAR QUESTIONS

Q1

If tan A and tan B are the roots of the quadratic equation x2 – px + q = 0, then the value of sin2 (A + B) is

Q2

If x2 – 4x + log1/2 a does not have two distinct roots, then the maximum value of a

Q3

If the roots of the equation bx2 + cx + a = 0 be expression, then for all real values of x, the expression 3b2 x2 + 6bcx + 2c2 is

Q4

If , for all x Ïµ R, then

Q5

If x is real, the maximum value of  is:

Q6

If the roots the equation ax2 + bx + c = are real and of opposite sign then the roots of the equation α (x – β)2 + β (x – α)2 = 0 are

Q7

abc are length of sides of an scalene triangle. If equation

           

has real and distinct roots, then the value of λ is given by:

Q8

A quadratic equation with rational coefficients can have

Q9

If the roots of ax2 + bx + c = 0 are in the ratio mn then

Q10

If the expression y2 + 2xy + 2x + my – 3 can be resolved into two rational factors, then m must be