If {vmatrix} 1+2x & -1 \\ 6 & 3-x {vmatrix} = -3, find the values of x.

Correct Answer is : x=4, −32x = 4, \; -3/2x=4,2−3

Correct Answer is : x=4, −32x = 4, \; -3/2x=4,2−3

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WAEC Further Mathematics 2015 Paper

Question : 26

Total: 40

\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3

x

Solution:

Concept:

Evaluating a

2 \times 2

determinant converts the equation into a quadratic in

x

Explanation:

Expand the determinant using

\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = (1+2x)(3-x) - (-1)(6) = -3

This simplifies to

(1+2x)(3-x) + 6 = -3

Expand:

3 - x + 6x - 2x^2 + 6 = -3

Combine like terms:

-2x^2 + 5x + 9 = -3

Rearrange:

-2x^2 + 5x + 12 = 0

Multiply through by

-1

2x^2 - 5x - 12 = 0

Factorise:

(2x+3)(x-4) = 0

Therefore,

2x+3 = 0

x-4 = 0

Hence,

x = -\frac{3}{2}

x = 4

Answer:

x = 4, \; -\frac{3}{2}

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