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Question

Find the value of m such that roots of the quadratic equation x2(m3)x+m=0 (mR) are positive

A
[9,)
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B
[1,9]
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C
(3,9)
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D
(,9]
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Solution

The correct option is A [9,)
Condition: When roots are positive :

(i) D0
(ii) Sum of roots >0
(iii) product of roots >0

Now, solve it one by one

(i) D0

(m3)24m0

m26m+94m0

m210m+9>

(m1)(m9)0

m(,1][9,)

(ii) Sum of roots >0

Sum of roots =(m3)>0

(m3)>0m>3

m(3,)

(iii) Product of roots >0

Product of roots =m1>0

m>0m(0,)

Now, taking intersection of all the three conditions, we get

m[9,)




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