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Question

Find the value of m such that roots of the quadratic equation x2(m3)x+m=0 (mR) are equal in magnitude but opposite in sign.

A
ϕ
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B
(1,3)
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C
None of the above.
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D
(3,9)
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Solution

The correct option is A ϕ
Condition : when root are equal in magnitude but opposite in sign,

(i) D>0 (ii) Sum of roots =0

(i) D>0

(m3)24m>0

m26m+94m>0

m210m+9>0

(m1)(m9)>0

m(,1)(9,)

(ii) Sum of roots =0

Sum of roots =(m3)=0m=3

Now, taking intersection of both the condition, we get

mϕ

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