If and , then the domain of the function…

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

If q2−4pr=0q^2-4pr=0 and p>0p>0, then the domain of the function f(x)=log⁡(px3+(p+q)x2+(q+r)x+r)f(x)=\log\left(px^3+(p+q)x^2+(q+r)x+r\right) is (a) R∖{−q2p}\mathbb{R}\setminus\left\{-\frac{q}{2p}\right\} (b) R∖[(−∞,−1]∪{−q2p}]\mathbb{R}\setminus\left[(-\infty,-1]\cup\left\{-\frac{q}{2p}\right\}\right] (c) R∖[(−∞,−1)∩{−q2p}]\mathbb{R}\setminus\left[(-\infty,-1)\cap\left\{-\frac{q}{2p}\right\}\right] (d) R\mathbb{R}

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