From the equation whose roots are x = 1/2 and -2/3

Correct Answer is : 6x2 + x - 2 = 0

Correct Answer is : 6x2 + x - 2 = 0

Test Index

WAEC Mathematics 2011 Paper

Question : 11

Total: 47

\frac{1}{2}

\frac{2}{3}

Solution:

Concept:

\alpha

and

\beta

are the roots of a quadratic equation, then the equation is

(x-\alpha)(x-\beta)=0

Explanation:

The given roots are

x=\frac{1}{2}

and

x=-\frac{2}{3}

Therefore, the equation is

\left(x-\frac{1}{2}\right)\left(x+\frac{2}{3}\right)=0

Expanding:

x^2+\frac{2}{3}x-\frac{1}{2}x-\frac{1}{2}\times\frac{2}{3}=0

Combine the

x

terms:

\frac{2}{3}x-\frac{1}{2}x=\frac{4x-3x}{6}=\frac{x}{6}

Constant term:

-\frac{1}{2}\times\frac{2}{3}=-\frac{1}{3}

So,

x^2+\frac{x}{6}-\frac{1}{3}=0

Multiplying the whole equation by

6

gives

6x^2+x-2=0

Answer:

6x^2+x-2=0

, which is option D.

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