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

 

Options

• p = 1, q = −2

• p = −1, q = −2

• p = −1, q = 2

• p = 1, q = 2

Answer 1

p = 1, q = −2

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

\[\therefore \text { Sum of roots } = p + q = - p\]

\[ \Rightarrow 2p + q = 0 . . . (1)\]

\[\text { Product of roots } = pq = q\]

\[ \Rightarrow q\left( p - 1 \right) = 0\]

\[ \Rightarrow p = 1, q = 0 \text { but } q \neq 0\]

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

\[2 + q = 0\]

\[ \Rightarrow q = - 2\]

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