Eric Nicholas K's answer to Arshath's Secondary 3 A Maths Singapore question.
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If a is a factor of k, while b and c are factors of a, then both b and c are also factors of k.
For the last part, we need to realise that f(x) can be expressed as the product of two quadratic factors, one of which is our original x^2 + 2x - 3 = 0 (with roots x = -3 and x = 1) and the other is x^2 + 4x + 5 = 0, which has no real roots since its discriminant is negative. Putting both together (two real roots from x^2 + 2x - 3 = 0 and no real root from x^2 + 4x + 5 = 0), the entire equation f(x) = 0 has two distinct real roots.
For the last part, we need to realise that f(x) can be expressed as the product of two quadratic factors, one of which is our original x^2 + 2x - 3 = 0 (with roots x = -3 and x = 1) and the other is x^2 + 4x + 5 = 0, which has no real roots since its discriminant is negative. Putting both together (two real roots from x^2 + 2x - 3 = 0 and no real root from x^2 + 4x + 5 = 0), the entire equation f(x) = 0 has two distinct real roots.
Date Posted:
4 years ago
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