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JAMB Mathematics 2017 Paper

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Question : 42

Total: 44

If α and β are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/α + 1/β

$\frac{-5}{3}$
$\frac{-2}{3}$
$\frac{1}{2}$
$\frac{5}{2}$

Solution:

Concept:

Use the sum and product of the roots of a quadratic equation.

Explanation:

For

3x^2 + 5x - 2 = 0

, compare with

ax^2 + bx + c = 0

.

Here

a = 3

,

b = 5

, and

c = -2

.

Sum of roots:

\alpha + \beta = -\frac{b}{a} = -\frac{5}{3}

.

Product of roots:

\alpha\beta = \frac{c}{a} = \frac{-2}{3}

.

Now rewrite the required expression:

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

.

Substitute the values:

\frac{1}{\alpha} + \frac{1}{\beta} = \frac{-\frac{5}{3}}{-\frac{2}{3}} = \frac{5}{2}

.

Answer:

\frac{5}{2}

Option D.

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