A) \[3{{x}^{2}}-5x-100=0\]
B) \[5{{x}^{2}}+3x+100=0\]
C) \[3{{x}^{2}}-5x+100=0\]
D) \[5{{x}^{2}}-3x-100=0\] \[5{{x}^{2}}-3x-100=0\]
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 = \[(3p-2q)\,(3q-2p)\] = \[9pq-6{{q}^{2}}-6{{p}^{2}}+4pq\] = \[13pq-2(3{{p}^{2}}+3{{q}^{2}})\] = \[13\left( \frac{-2}{3} \right)-2(5p+2+5q+2)\] = \[13\,\left( \frac{-2}{3} \right)-2\left[ 5\,\left( \frac{5}{3} \right)+4 \right]\] = \[\frac{-26}{3}-2\,\left[ \frac{25}{3}+4 \right]\]= \[\frac{-100}{3}\] Hence, equation is \[3{{x}^{2}}-5x-100=\]0.
You need to login to perform this action.
You will be redirected in
3 sec
