The roots of the quadratic equation \(x^2 + kx + 16 = 0\) are real and equal. Complete the following activity to find the value of \(k\).Solution :Comparing with \(ax^2 + bx + c = 0\), \(a = 1,\ b =\) ____, \(c = 16\)Since the roots are real and equa…

Q.3 (A)(ii) The roots of the quadratic equation \(x^2 + kx + 16 = 0\) are real and equal. Complete the following activity to find the value of \(k\).

Solution :

Comparing with \(ax^2 + bx + c = 0\), \(a = 1,\ b =\) ____, \(c = 16\)
Since the roots are real and equal, \(b^2 - 4ac =\) ____
\(\therefore k^2 - 4 \times 1 \times\) ____ \(= 0\)
\(\therefore k^2 =\) ____
\(\therefore k =\) ____ or \(k =\) ____

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: \(k = 8\) or \(k = -8\)

\(a = 1,\ b = k,\ c = 16\).

Roots are real and equal, so \(\Delta = b^2 - 4ac = 0\).

\(k^2 - 4(1)(16) = 0 \Rightarrow k^2 = 64 \Rightarrow k = 8\) or \(k = -8\).

Check: \(k = 8\) gives \((x + 4)^2 = 0\) and \(k = -8\) gives \((x - 4)^2 = 0\), both with equal roots.

Blanks in order: k, 0, 16, 64, 8, −8.

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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The roots of the quadratic equation \(x^2 + kx + 16 = 0\) are real and equal. Complete the following activity to find the value of \(k\).Solution :Comparing with \(ax^2 + bx + c = 0\), \(a = 1,\ b =\) ____, \(c = 16\)Since the roots are real and equa…

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