Question

### Gauthmathier7796

Grade 9 · 2020-11-04

For the equation 2x-1=-\sqrt{2-x}, find the sum of the roots. （ ）

Good Question (63)

Answer

4.6(190) votes

### Gauthmathier0399

Grade 9 · 2020-11-04

Answer

A

Explanation

2x-1=-\sqrt{2-x}

\Rightarrow (2x-1)^{2}=2-x

\Rightarrow 4x^{2}-3x-1=0

\Rightarrow (4x+1)(x-1)=0

\Rightarrow x=-\dfrac{1}{4} or 1

Checking answers by plugging these x-values into the original equation, shows that -\dfrac{1}{4} is a solution, but 1 is not. Therefore the sum of the roots is -\dfrac{1}{4}.

\Rightarrow (2x-1)^{2}=2-x

\Rightarrow 4x^{2}-3x-1=0

\Rightarrow (4x+1)(x-1)=0

\Rightarrow x=-\dfrac{1}{4} or 1

Checking answers by plugging these x-values into the original equation, shows that -\dfrac{1}{4} is a solution, but 1 is not. Therefore the sum of the roots is -\dfrac{1}{4}.

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