Find the equation whose roots are 3/4 and -4

Correct Answer is : 4x2 + 13x - 12 = 0

Correct Answer is : 4x2 + 13x - 12 = 0

Test Index

WAEC Mathematics 2015 Paper

Question : 9

Total: 45

\frac{3}{4}

and -4

Solution:

Concept:

\alpha

and

\beta

are the roots, the quadratic equation is

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

Explanation:

Given roots are

\frac{3}{4}

and

-4

Sum of roots

= \frac{3}{4} + (-4) = \frac{3-16}{4} = -\frac{13}{4}

Product of roots

= \frac{3}{4} \times (-4) = -3

Thus, the equation is

x^2 - \left(-\frac{13}{4}\right)x + (-3) = 0

So,

x^2 + \frac{13}{4}x - 3 = 0

Multiplying the entire equation by

4

gives

4x^2 + 13x - 12 = 0

Answer:

The correct option is C:

4x^2 + 13x - 12 = 0

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