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WAEC Further Mathematics 2021 Paper

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Question : 9

Total: 38

If α and β are the roots of 3x

^2

- 7x + 6 = 0, find

\;\frac{1}{\alpha}

\;\frac{1}{\beta}

$\;\frac{7}{6}$
$\;\frac{7}{3}$
$\;\frac{14}{5}$
$\;\frac{14}{3}$

Solution:

Concept:

For a quadratic equation, use the sum and product of roots to simplify the required expression.

Explanation:

The given equation is

3x^2 - 7x + 6 = 0

.

For

ax^2 + bx + c = 0

, sum of roots is

\alpha + \beta = -\frac{b}{a}

and product of roots is

\alpha\beta = \frac{c}{a}

.

Here,

a = 3

,

b = -7

,

c = 6

.

So,

\alpha + \beta = -\frac{-7}{3} = \frac{7}{3}

.

And,

\alpha\beta = \frac{6}{3} = 2

.

Now,

\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta}

.

Substitute the values:

\frac{\frac{7}{3}}{2} = \frac{7}{3} \times \frac{1}{2} = \frac{7}{6}

.

Answer:

\frac{7}{6}

Option A.

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