Complex Numbers And Quadratic Equations question 622
Question: If $ 3p^{2}=5p+2 $ and $ 3q^{2}=5q+2 $ where $ p\ne q $ , then the equation whose roots are $ 3p-2q $ and $ 3q-2p $ is [Kerala (Engg.) 2005]
Options:
A) $ 3x^{2}-5x-100=0 $
B) $ 5x^{2}+3x+100=0 $
C) $ 3x^{2}-5x+100=0 $
D) $ 5x^{2}-3x-100=0 $ $ 5x^{2}-3x-100=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given roots are $ 3p-2q $ and $ 3q-2p $ . Sum of roots = $ (3p-2q)+(3q-2p) $ = $ (p+q)=\frac{5}{3} $ Product of roots = $ (3p-2q)(3q-2p) $ = $ 9pq-6q^{2}-6p^{2}+4pq $ = $ 13pq-2(3p^{2}+3q^{2}) $ = $ 13( \frac{-2}{3} )-2(5p+2+5q+2) $ = $ 13( \frac{-2}{3} )-2[ 5( \frac{5}{3} )+4 ] $ = $ \frac{-26}{3}-2[ \frac{25}{3}+4 ] $ = $ \frac{-100}{3} $ Hence, equation is $ 3x^{2}-5x-100= $ 0.
BETA
