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Determine the nature of roots of the following quadratic equation.Activity :\(m^2 + 2m + 9 = 0\)\(a = \) ____ , \(b = 2\), \(c = 9\)\(b^2 - 4ac = 2^2 - 4 \times 1 \times \) ____\(= \) ____ \(- 36\)\(\therefore b^2 - 4ac = \) ____\(\therefore b^2 - 4a…

Q.2 (A)(ii) Determine the nature of roots of the following quadratic equation.

Activity :

\(m^2 + 2m + 9 = 0\)

\(a = \) ____ , \(b = 2\), \(c = 9\)

\(b^2 - 4ac = 2^2 - 4 \times 1 \times \) ____

\(= \) ____ \(- 36\)

\(\therefore b^2 - 4ac = \) ____

\(\therefore b^2 - 4ac < 0\)

\(\therefore\) Roots of quadratic equation are not real.

1 answer

Best answer

Answer: \(a = 1\), \(c = 9\), \(2^2 = 4\) so \(4 - 36 = -32\), and \(b^2 - 4ac = -32 < 0\); the roots are not real (imaginary).

Comparing \(m^2 + 2m + 9 = 0\) with \(am^2 + bm + c = 0\) : \(a = 1\), \(b = 2\), \(c = 9\).

\(b^2 - 4ac = 2^2 - 4 \times 1 \times 9 = 4 - 36 = -32\).

\(\therefore b^2 - 4ac = -32 < 0\), so the roots of the quadratic equation are not real.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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