2024 ACJC H1 Q2
2024 ACJC H1 Q2
5 marks
Find the set of values of \(k\) for which
\[(k^2 + 36)x^2 + (k - 6)x + 0.5 \ge 0\]
for all real values of \(x\).[4]
Hence find the set of values of \(k\) for which the expression
\[\ln[(k^2 + 36)x^2 + (k - 6)x + 0.5]\]
is defined for all real values of \(x\).[1]
Solution:
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Answer:Nonnegative quadratic for all \(x\): \(k\in\mathbb R\). Logarithm defined for all \(x\): \(k\in\mathbb R\setminus\{-6\}\).
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