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Sum and Product of Roots of a Quadratic Equation

If α and ...

Question

If $α$ and $β$ are roots of the quadratic equation $x^{2} - 2 x + 3 = 0$ then quadratic equation whose roots are $\frac{α - 1}{α + 1}, \frac{β - 1}{β + 1}$ is:

A

3 x^{2} + 2 x + 1 = 0.

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B

3 x^{2} - 2 x + 1 = 0.

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C

2 x^{2} - 3 x - 1 = 0.

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D

None of these

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Solution

The correct option is B $3 x^{2} - 2 x + 1 = 0.$

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Similar questions

α

β

x^{2} - 2 x + 3 = 0

, then the equation whose roots are

\frac{α - 1}{α + 1}

\frac{β - 1}{β + 1}

α

β

are the roots of the equation

3 x^{2} + 2 x + 1 = 0

, then the equation whose roots are

α + β^{- 1}

β + α^{- 1}

Q. If the quadratic equation

3 x^{2} + 4 x + 5 = 0

α

β

then the equation whose roots are

\frac{1}{α}

\frac{1}{β}

α

β

are the positive roots of a quadratic equation such that

| α - β | = 1

\frac{α}{β} + \frac{β}{α} = \frac{5}{2}

, then the quadratic equation is

α, β

are the roots of

3 x^{2} - 2 x + 1 = 0

, then the equation whose roots are

- \frac{α}{3}, - \frac{β}{3}

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Sum and Product of Roots of a Quadratic Equation

Standard X Mathematics

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