An equation equivalent to the quadratic equat | vedclass

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Question

(D) The given quadratic equation is $x^{2}-6x+5=0$.Factoring the quadratic expression,we get $(x-5)(x-1)=0$.This implies the roots are $x=5$ and $x=1$

Vedclass · Accepted Answer

$|x-3|=2$

Vedclass · Answer

(D) The given quadratic equation is $x^{2}-6x+5=0$.Factoring the quadratic expression,we get $(x-5)(x-1)=0$.This implies the roots are $x=5$ and $x=1$.Now,consider the equation $|x-3|=2$.By the definition of absolute value,this splits into two cases:Case $1$: $x-3=2 \implies x=5$.Case $2$: $x-3=-2 \implies x=1$.Since both equations have the same solution set $\{1, 5\}$,they are equivalent.

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

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