Question

${a}^{2} x + ( {a}^{2} - 1)x - a$
Resolve into factors
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Answer 1

Explanation:

Example 1.

2x2 - 5x - 12 = 0.

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

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

Square Root Principle

If x2 = k, then x = ± sqrt(k).

Example 2.

x2 - 9 = 0.

x2 = 9.

x = 3, or x = -3.

Example 3.

Example 4.

x2 + 7 = 0.

x2 = -7.

x = ± .

Note that = = , so the solutions are

x = ± , two complex numbers.