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WAEC Further Mathematics 2011 Paper

Question : 29

Total: 40

\binom{3x}{2} = 15

, find the value of x?

Solution:

Concept:

Expanding the binomial coefficient and solving the resulting quadratic equation.

Explanation:

Use the standard form

\binom{n}{2}=\frac{n(n-1)}{2}

with

n=3x

So,

\binom{3x}{2}=\frac{3x(3x-1)}{2}=15

Multiply both sides by 2:

3x(3x-1)=30

Expand and simplify:

9x^{2}-3x-30=0

Divide the equation by 3:

3x^{2}-x-10=0

Factorise:

(x-2)(3x+5)=0

Thus,

x=2

x=-\frac{5}{3}

Since

\binom{3x}{2}

requires a valid non-negative integer value for

3x

, reject

x=-\frac{5}{3}

Answer:

x=2

, option A.

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