Question

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

Solution

Correct option is

Have negative real parts

We have D = b2 – 4ac. If D ≥ 0, then the roots of the equation are given by

                       

As D = b2 – 4ac < b2 (∵ a > 0 , c > 0), it follows that the roots of the quadratic equation are negative. In case D < 0, the roots of the equation are given by

                        

which have negative real parts

SIMILAR QUESTIONS

Q1

If ax2 + bx + cabc Ïµ R has no real zeros, and if c < 0, then,

Q2

If x is real, then the maximum value of    

                                                                           

Q3

If both the roots of the equation x2 – 6ax + 2 – 2a + 9a2 = 0 exceed 3, then

Q5

Let α, β be the roots of the equation x2 – ax + b = 0 and An = αn + βn

Q6

Let f (x) = ax2 + bx + cabc Ïµ R. if f (x) takes real values for real values of x and non – real values for non – real values of x, then.

Q7

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

Q8

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

Q9

If x is real, and 

Q10

Let abc be non – zero real number such that

               

         

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