If α, β are the roots of equation x²-5 x+6=0 and α>β then the equation with roots (α β+α+β) and (α β-α-β) is

Correct Answer is : x2−12x+11=0x²-12 x+11=0x2−12x+11=0

Correct Answer is : x2−12x+11=0x²-12 x+11=0x2−12x+11=0

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Question : 27 of 39

Marks: +1, -0

\alpha, \beta

x^{2}-5 x+6=0

\alpha>\beta

(\alpha \beta+\alpha+\beta)

(\alpha \beta-\alpha-\beta)

Solution:

Concept:

Use the given quadratic to find the roots; then compute the new roots and form the quadratic.

Explanation:

The equation

x^{2}-5x+6=0

factors as

(x-2)(x-3)=0

, so roots are

2

and

3

Given

\alpha>\beta

, let

\alpha=3

\beta=2

Compute

\alpha\beta=6

and

\alpha+\beta=5

First new root:

\alpha\beta+\alpha+\beta = 6+5 = 11

Second new root:

\alpha\beta-\alpha-\beta = 6-5 = 1

The quadratic with roots

11

and

1

x^{2} - (11+1)x + (11\cdot1) = x^{2} - 12x + 11 = 0

Answer:

x^{2}-12x+11=0

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