WAEC 2010 Mathematics · Question 44

If the sum of the roots of the equation (x - p)(2x + 1) = 0 is 1, find the value of x

Options

A.1 $\frac{1}{2}$
B. $\frac{1}{2}$
C.- $\frac{3}{2}$
D.-1 $\frac{1}{2}$

Answer: A. 1 $\frac{1}{2}$

Explanation written with AI and checked against the answer key

The equation (x - p)(2x + 1) = 0 has roots x = p and x = -1/2. Step 1: Use the sum of the roots p + (-1/2) = 1, so p = 3/2 = 1½. Step 2: Interpret "find the value of x" The question is worded poorly. The roots are x = 3/2 and x = -1/2. Only one of these appears in the options: 1½ (option A). The value p = 1½ also matches option A, which is the unknown the question most likely intends. Check: 3/2 + (-1/2) = 1 ✓ The question asks for "the value of x" but really means the value of p, the unknown in the equation. Both readings lead to 1½, since x = 3/2 is one of the roots. Tip: For a question like this, find the roots of each factor first (set each bracket to zero). Then use the given sum or product to find the unknown. If the wording is unclear, check which option matches your working.

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If the sum of the roots of the equation (x - p)(2x + 1) = 0 is 1, find the value of x

Options

Answer: A. 112\frac{1}{2}21​

Answer: A. 1 $\frac{1}{2}$