﻿   Let P, Q, R be defined as        P = a2b + ab2 – a2c – ac2,        Q = b2c + bc2 – a2b – ac2        R = a2c + c2a – c2b – cb2 Where a, b, c are all + ive and the equation Px2 + Qx + R = 0 has equal roots then a, b, c are in : Kaysons Education

# Let P, Q, R Be Defined As        P = a2b + ab2 – a2c – ac2,        Q = b2c + bc2 – a2b – ac2        R = a2c + c2a – c2b – cb2 Where a, b, c are All + Ive And The Equation Px2 + Qx + R = 0 Has Equal Roots Then a, b, c are In

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

H.P.

Hence 1 is a root of Px2 + Qx + R = 0

Since it has equal roots therefore roots are 1, 1.

or  abc are in H. P.

#### SIMILAR QUESTIONS

Q1

Q2

If the roots of the equation x2 + px – q = 0 are tan 300 and tan 150, then the value of 2 + q – p is

Q3

If α, β, γ are the roots of the equation x3 + ax + b = 0, then

Q4

Let α, β be the roots of x2 – x + p = 0 and γ, δ be the roots of x2 – 4x + = 0. If α, β, γ, δ are in G.P., then the integral values of p and qrespectively, are

Q5

Let α and β are the roots of equation x2 + x + 1 = 0. The equation whose roots are α19, β7 is

Q6

If x2 + x + 1 is a factor ax3 + bx2 + cx + d, then the real root of ax3 + bx2cx + d = 0 is

Q7

If one root of the equation (a2 – 5a + 3)x2 + (3a – 1)x + 2 = 0 be double the other, then the value of α is:

Q8

For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

Q9

If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

Q10

If b > a, then the equation (x – a) (x – b) – 1 = 0, has