Question

If all the roots of x3 + px + q = 0 pq Ïµ R q ≠ 0 are real, then

Solution

Correct option is

p < 0

If α, β, γ are the roots of

x3 + px + q = 0, then

α + β + γ = 0, βγ + γα + αβ = p, αβγ = – q

As q ≠ 0, none of α, β, γ is zero. Now, use

2p = (α + β + γ)2 – (α2 + β2 + γ2) < 0

SIMILAR QUESTIONS

Q1

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

                                            

Q2

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

Q3

If a ≤ 0, the number of real roots of

                                                           

Q4

 

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

then the equation

                  

Q5

If three distinct real number ab and c satisfy

                                         

Where p Ïµ R, then value of b c + ca + a b is

Q6

The number of integral roots of the equation 

is

Q7

The product of roots of 

Q8

Let S denote the set of all values of the parameter a for which

                        

has no solution, then S equals

Q9

The number of roots of the equation 

Q10

Let S denote the set of all real value of q for which the roots of the equation

                          x2 – 2ax + a2 – 1 = 0          ...(1)

lie between 5 and 10, then S equals