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Question

For what value/s of k, the quadratic equation 2kx2+6kx+9=0 has no real roots?

A
0<k<2
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B
k=0
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C
k>2
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D
2<k<0
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Solution

The correct option is A 0<k<2
2kx2+6kx+9=0

a=2k,b=6k,c=9

Since the quadratic equation has no real roots,

D=b24ac<0

(6k)24×2k×9<0

36k272k<0

k(k2)<0

It is of the form(xa)(xb)<0anda<b,then

a<x<b

0<k<2

Thus, for all values of k in (0,2), the quadratic equation has no real roots

(a) is correct

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