Question

2. Determine the roots of the equation x2 – 3x - m(m + 3) = 0, where m is any constant.​

Answer 1

Determine the roots of quadratic equation:

x² - 3x - m(m + 3) = 0

On simplifying the above equation;

x² - 3x - m² - 3m = 0

On grouping like terms,

⇒ x² - m² - 3x - 3m = 0

Split x² - m² using a² - b² = (a + b) (a - b)

⇒ (x + m) (x - m) -3(x + m)

Now, the factors are (x + m) or (x - m - 3)

x + m = 0 OR (x - m - 3) = 0

→ x = 0 - m OR → x - m = 3

→ x = -m OR → x = m + 3

∴ The roots of the equation are (-m) and (m + 3)

Answer 2

Hope it helps all.

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