Question

If a ≤ 0, the number of real roots of

                                                           

Solution

Correct option is

All four real roots

Put x – a = t and rewrite (1) as

                   

If t < 0, we get t2 + 4a2 = 0 

Not possible. Therefore t ≥ 0.

Thus, (2) gives t2 + 4at + 4a2 = 0

⇒ t = – 2a

⇒ x = – a

SIMILAR QUESTIONS

Q1

If α, β, γ are such that α + β + γ = 2, α2 + β2 + γ2 = 6, α3 + β3 + γ3 = 8, then α4 + β4 + γ4 is

Q2

The condition that the equation  has real roots that are the equal in magnitude but opposite in sign is

Q3

If x is real, and 

Q4

Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax2 + bx +c = 0

Q5

Let abc be non – zero real number such that

               

         

Then the quadratic equation ax2 + bx + c = 0 has

Q7

The equation 3x–1 + 5x–1 = 34 has

Q8

If the harmonic mean between roots of   is 4 then b equals

                                            

Q9

In a triangle PQRR = π/4. If tan (P/3) and tan (Q/3) are the roots of the equation ax 2 + bx + c = 0, then

Q10

 

Let (a1a2a3a4a5) denote a rearrangement of (3, – 5, 7 4, – 9),

then the equation