Question: Directions: In the given questions, two equations numbered I and II are given. Solve both the equations and mark the appropriate answer.
I. $ 15x^{2}-29x-14=0 $
II. $ 6y^{2}-5y-25=0 $
Options:
A) $ x>y $
B) $ x\ge y $
C) $ x<y $
D) $ x\le y $
E) Relationship between x and y cannot be determined
Show Answer
Answer:
Correct Answer: E
Solution:
- I. $ 15x^{2}-29x-14=0 $
$ x _1=\frac{29+\sqrt{841+60\times 14}}{30} $
$ =\frac{29+41}{30}=\frac{70}{30}=\frac{7}{3} $
or $ x _2=\frac{29-\sqrt{1681}}{30} $
$ \Rightarrow $ $ x _2=\frac{29-41}{30}=\frac{-12}{30}=\frac{-,2}{5} $
$ \Rightarrow $ $ x=\frac{7}{3}, $ $ \frac{-,2}{5} $
II. $ 6y^{2}-5y-25=0 $
$ y _1=\frac{5+\sqrt{25-4\times 6\times -25}}{12} $
$ =\frac{5+\sqrt{625}}{12}=\frac{30}{12}=\frac{5}{2} $
or $ y _2=\frac{5-\sqrt{25-4\times 6\times -,25}}{12} $
$ \Rightarrow $ $ y _2=\frac{5-\sqrt{625}}{12}=\frac{-,20}{12}=\frac{-,5}{3} $
$ \Rightarrow $ $ y=\frac{5}{2}, $ $ \frac{-,5}{3} $
So, relationship between x and y cannot be determined.
BETA
