Find the range of values of the constant $k$ for which $k(x^2 + x) + 2(x^2 + x + 1) = 0$ has no

Question

Find the range of values of the constant $k$ for which $k(x^2 + x) + 2(x^2 + x + 1) = 0$ has no real roots.[4] Hence, explain why $-(x^2 + x) + 2(x^2 + x + 1)$ is always positive.[2]

Accepted Answer

(a) $-2\le k<6$; the quadratic case alone gives $-2<k<6$. (b) No real roots and positive coefficient of $x^2$; always positive.

2025 PHS P2 Q5

2025 PHS P2 Q5

Solution:

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