Find the value of $k$ for which the quadratic equation $4x^2 + kx + 1 = 0$ has real and equal roots.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
For real and equal roots, the discriminant must be zero:
$$b^2 - 4ac = 0$$
Here, $a = 4$, $b = k$, $c = 1$.
$$k^2 - 4(4)(1) = 0$$
$$k^2 = 16$$
$$k = \pm 4$$
Source: Chapter 4, Section 4.4 Nature of Roots
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Explanation
- The key condition for equal roots is $b^2 - 4ac = 0$. Examiners expect you to state this condition first, then substitute correctly.
- Both $+4$ and $-4$ must be written; missing either loses a mark.
- No need to verify separately — finding $k$ is sufficient for 2 marks.