﻿ If all the roots of x3 + px + q = 0 p, q Ïµ R q ≠ 0 are real, then : Kaysons Education

# If All The Roots Of x3 + px + q = 0 p, q Ïµ R q ≠ 0 Are Real, Then

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## Question

### 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