Question

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

Solution

Correct option is

Real and of opp. sign

Given b2 = 4ac ≥ 0 and product  ive

The given equation is

 

 

 

        

Δ is clearly + ive as  is – ive. Hence the roots are real and their product being  ive so that they are of opposite sign.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

If , for all x Ïµ R, then

Q9

If x is real, the maximum value of  is:

Q10

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

           

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