﻿ Let α,β be the roots of the equation x2 – px + r = 0 and  2β be the roots of the equation x2 – qx + r = 0. Then the value of r is : Kaysons Education

# Let α,β Be The Roots Of The Equation x2 – px + r = 0 And  2β Be The Roots Of The Equation x2 – qx + r = 0. Then The Value Of r is

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## Question

### Solution

Correct option is

We have the following relations

α + β = p…………….(1)

αβ = r………………..(2)

………….(3)

…….(4)

Solving (1) and (3) for α and β, we get

#### SIMILAR QUESTIONS

Q1

Let P, Q, R be defined as

P = a2b + ab2 – a2c – ac2,

Q = b2c + bc2 – a2b – ac2

R = a2c + c2a – c2b – cb2

Where abc are all + ive and the equation Px2 + Qx + R = 0 has equal roots then abc are in

Q2

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

Q3

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

Q4

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:

Q5

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

Q6

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

Q7

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

Q8

If α and β (α < β), are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then

Q9

If 1 lies between the roots of the equation 3x2 – 3 sin α x – 2 cos2 α = 0 then α lies in the interval

Q10

The number of real roots of the equation (x + 3)4 + (x + 5)4 = 16 is