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Question

x2(m3)x+m=0(mR) be a quadratic equation. Find the value of m for which. Exactly one root lies in the interval (1,2) :

A
(0,45)
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B
(2,3)
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C
(3,)
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D
(10,)
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Solution

The correct option is C (10,)
f(x)=x2(m3)x+m=0

One root lies between (1,2)
D>0
(m3)24m>0
m26m+94m>0
m210m+9m>0
(m9)(m1)>0
m(,1)(9,)

Condition 2
Since, one root has to lie between (1,2)

f(1)f(2)<0
(m+3+m)(42m+6+m)<0
3(10m)<0
m10>0
m(10,)

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