The integer m for which the inequality x^{2}-2(4m-1)x+15m^{2}-2m-7> 0 is valid for x any , is

  • Option 1)

    2

  • Option 2)

    3

  • Option 3)

    4

  • Option 4)

    None of these

 

Answers (1)

As learnt in concept

Complex Roots with non - zero Imaginary part -

D= b^{2}-4ac< 0

- wherein

ax^{2}+bx+c= 0

is the quadratic equation

 

 x^{2}-2(4m-1)x+15m^{2}-2m-7>0

Here D\leqslant 0

Thus 4(4m-1)^{2}-4(15m^{2}-2m-7)\leqslant 0

(16m^{2}+1-8m-15m^{2}+2m+7)\leqslant 0

m^{2}-6m+8\leqslant 0

m^{2}-4m-2m+8\leqslant 0

m\in [2,4]

Thus m can be 2, 3,4


Option 1)

2

This is incorrect option

Option 2)

3

This is correct option

Option 3)

4

This is incorrect option

Option 4)

None of these

This is incorrect option

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