The roots of a quadratic equation are -1/2 and 2/3. Find the equation.

Correct Answer is : 6x2−x−2=06x² - x - 2 = 06x2−x−2=0

Correct Answer is : 6x2−x−2=06x² - x - 2 = 06x2−x−2=0

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WAEC Mathematics 2017 Paper

Question : 28

Total: 49

\frac{-1}{2}

\frac{2}{3}

. Find the equation.

Solution:

Concept:

\alpha

and

\beta

are roots of a quadratic equation, then the equation is

x^2 - (\alpha+\beta)x + \alpha\beta = 0

Explanation:

For the roots

\alpha = \frac{-1}{2}

and

\beta = \frac{2}{3}

, first find the sum of the roots:

\alpha + \beta = \frac{-1}{2} + \frac{2}{3} = \frac{-3+4}{6} = \frac{1}{6}

Then find the product of the roots:

\alpha\beta = \frac{-1}{2} \times \frac{2}{3} = \frac{-2}{6} = \frac{-1}{3}

Substitute into the quadratic formula:

x^2 - \left(\frac{1}{6}\right)x + \left(\frac{-1}{3}\right) = 0

That is,

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

Multiply through by 6 to remove fractions:

6x^2 - x - 2 = 0

Answer:

6x^2 - x - 2 = 0

(Option B)

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