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Question

Which of the following quadratic equations does not have both of its roots lying in the range of y=3sinx?


Your Answer
A
x24=0
Your Answer
B
x2+x2=0
Your Answer
C
3x2x=0
Correct Answer
D
x22x8=0

Solution

The correct option is D x22x8=0
We know
1sinx1
33sinx3
Range of y=3sinx
y[3,3]

Finding the roots of the quadratic equations,
x24=0
x=±2[3,3]

x2+x2=0(x+2)(x1)=0
x=1,2[3,3]

3x2x=0
x=0,13[3,3]

x22x8=0(x4)(x+2)=0
x=2,4
x=4[3,3]

Therefore, the roots of equation x22x8=0 does not lie between [3,3].

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