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Algebra of Roots of Quadratic Equations

If α is the g...

Question

If $α$ is the greater root of $x^{2} - 5 x + 4 = 0$ and $α + m = 2$ , then the value of $m$ is

A

- 3

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B

2

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C

3

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D

- 2

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Solution

The correct option is D $- 2$
Given quadratic equation is
$x^{2} - 5 x + 4 = 0 \Rightarrow x^{2} - 4 x - x + 4 = 0 \Rightarrow x (x - 4) - 1 (x - 4) = 0 \Rightarrow (x - 4) (x - 1) = 0 \Rightarrow x = 1, 4$
As $α$ is the greater root, so
$α = 4 \Rightarrow α + m = 2 ∴ m = - 2$

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Algebra of Roots of Quadratic Equations

Standard XIII Mathematics

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