Search any question & find its solution
Question:
Answered & Verified by Expert
If $p$ and $q$ are distinct prime numbers and if the equation $x^2-p x+q=0$ has positive integers as its roots, then the roots of the equation are
Options:
Solution:
1530 Upvotes
Verified Answer
The correct answer is:
1,2
Given, $p$ and $q$ are distinct prime.
Let $p=3$ and $q=2$
$\therefore$ Given equation becomes
$$
\begin{array}{rlrl}
& x^2-3 x+2 & =0 \\
\Rightarrow & x-2 x-x+2 & =0 \\
\Rightarrow & x(x-2)-1(x-2) & =0 \\
\Rightarrow & & (x-1)(x-2) & =0 \\
\Rightarrow & x & =1,2
\end{array}
$$
Let $p=3$ and $q=2$
$\therefore$ Given equation becomes
$$
\begin{array}{rlrl}
& x^2-3 x+2 & =0 \\
\Rightarrow & x-2 x-x+2 & =0 \\
\Rightarrow & x(x-2)-1(x-2) & =0 \\
\Rightarrow & & (x-1)(x-2) & =0 \\
\Rightarrow & x & =1,2
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.