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Question

The values of m for which roots of the quadratic equation x2+(2m+3)xm2=0 lies on either side of 3.

A
(0,6)
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B
[34,0]
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C
(6,0)
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D
[34,]
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Solution

The correct option is A (0,6)
Let f(x)=x2+(2m+3)xm2

On comparing with standard quadratic equation y=ax2+bx+c we get a=1,b=2m+3,c=m2.

Since a<0
Downward opening parabola

Required conditions are
(i) D>0 (Since there are 2 unequal roots)
D=b24ac>0
D=(2m+3)24.(1).(m2)>0
12m+9>0
m>34
​​​​m(34,)(1)

(ii)f(3)>0
(3)2+(2m+3)(3)m2>0
m(m6)<0
m(0,6)(2)

Final set of solution will be the intersection of 1,2.
m(34,)(0,6)

m(0,6)

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