Question

The value of p and q (p ≠ 0, q ≠ 0) for which p, q are the roots of the equation $x^2+px+q=0$ are
(a) p = 1, q = −2
(b) p = −1, q = −2
(c) p = −1, q = 2
(d) p = 1, q = 2

Answer 1

(a) p = 1, q = −2

It is given that, p and q (p ≠ 0, q ≠ 0) are the roots of the equation $x^2+px+q=0$.

$$\begin{gathered} \therefore \mathrm{Sum}\mathrm{of}\mathrm{roots}=p+q=-p \\ \Rightarrow 2p+q=0...\left(1\right) \end{gathered}$$

$$\begin{gathered} \mathrm{Product}\mathrm{of}\mathrm{roots}=pq=q \\ \Rightarrow q\left(p-1\right)=0 \\ \Rightarrow p=1,q=0\mathrm{but}q\ne 0 \end{gathered}$$

Now, substituting p = 1 in (1), we get,

$$\begin{gathered} 2+q=0 \\ \Rightarrow q=-2 \end{gathered}$$

Disclaimer: The solution given in the book is incorrect. The solution here is created according to the question given in the book.