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Question

For the equation 2x3x2āˆ’x+2āˆ’7x3x2+5x+2=1, which of the following statements(s) is/are?

A
It has 4 real roots.
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B
It has 2 real roots.
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C
Sum of roots is 3
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D
Sum of roots is 113
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Solution

The correct options are
B It has 2 real roots.
C Sum of roots is 3
2x3x2x+27x3x2+5x+2=123x+2x173x+2x+5=1
Assuming 3x+2x=t
2t17t+5=12t+107t+7=(t1)(t+5)t2+4t5=5t+17t2+9t22=0(t+11)(t2)=0t=11,2

When t=11
3x+2x=113x2+11x+2=0D=12124>0
Two real and distinct root
Sum of roots =113

When t=2
3x+2x=23x22x+2=0D=424<0
No real roots.
Sum of roots =23

Therefore,
Sum of the roots =113+23=3
The given equation has 2 real roots.

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