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WAEC Mathematics 2024 Paper

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Question : 19

Total: 50

Find the quadratic equation whose roots are

\;\frac{2}{3}

and - 1

3x $^2$ - x - 2 = 0
3x $^2$ + x + 2 = 0
3x $^2$ + x - 2 = 0
3x $^2$ + x - 1 = 0

Solution:

Concept:

For roots

\alpha

and

\beta

, the quadratic equation is

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

.

Explanation:

Given roots are

\alpha = \frac{2}{3}

and

\beta = -1

.

Sum of roots:

\alpha + \beta = \frac{2}{3} + (-1) = \frac{2}{3} - 1 = -\frac{1}{3}

.

Product of roots:

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

.

Substitute into the standard equation:

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

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

Multiply through by

3

:

3x^2 + x - 2 = 0

Answer:

3x^2 + x - 2 = 0

(Option C).

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