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Factor Theorem

An equation e...

Question

An equation equivalent to the quadratic equation $x^{2} - 6 x + 5 = 0$ is

6 x^{2} - 5 x + 1 = 0

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

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5 x^{2} - 6 x + 1 = 0

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| x - 3 | = 2

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Solution

The correct option is D $| x - 3 | = 2$
Given equation is: $x^{2} - 6 x + 5 = 0$
$x^{2} - 5 x - x + 5 = 0$
$x (x - 5) - 1 (x - 5) = 0$
$(x - 1) (x - 5) = 0$
$x = 1$ and $x = 5$
Now
$x = 1$
$x - 3 = - 2$
$x - 3 = - 2$ ...(i) and
$x = 5$
$x = 3 + 2$
$x - 3 = 2$ ...(ii)
Combining i and ii, we get
$x - 3 = | 2 |$
or
$| x - 3 | = 2$

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