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Let f\left ( x \right )= x^{2}+2\left ( a-1 \right )x+\left ( a+5 \right ), then the values of 'a' for which f\left ( x \right )= 0 doesn't have two real and distinct roots is 

  • Option 1)

    (-1,4]

  • Option 2)

    [-1,4)

  • Option 3)

    (-1,4)

  • Option 4)

    [-1,4]

 

Answers (1)

\because f(x)=0   doesn't have real and distinct roots, so either it will have real and equal roots or imaginary roots .

\\*So\; \; D\leq 0\Rightarrow 4(a^{2}-2a+1)-4(a+5)\leq 0\\*\Rightarrow (a-4)(a+1)\leq 0\Rightarrow a\epsilon \left [ -1,4 \right ]

 

Quadratic Expression Graph when a > 0 & D = 0 -

Real and Equal roots of

f\left ( x \right )= ax^{2}+bx+c

& D= b^{2}-4ac

- wherein

 

 


Option 1)

(-1,4]

This is incorrect

Option 2)

[-1,4)

This is incorrect

Option 3)

(-1,4)

This is incorrect

Option 4)

[-1,4]

This is correct

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