Find the set of values of 'a' for which the given condition is true (a-1) (a-3)(a+5) > 0

  • Option 1)

    \left ( -5,1 \right ) \cup \left ( 3,\infty \right )

  • Option 2)

    (-1, 5)

  • Option 3)

    \left [ -5,1 \right ] \cup \left [ 3,\infty \right)

  • Option 4)

    None of these. 

 

Answers (1)

As learnt in concept

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

Real and distinct roots of

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

& D= b^{2}-4ac

- wherein

 

 (a-1)(a-3)(a+5)>0

According to wavy curve method, 

a\in (-5,1)\cup (3,\infty)

 


Option 1)

\left ( -5,1 \right ) \cup \left ( 3,\infty \right )

Correct option

Option 2)

(-1, 5)

Incorrect option

Option 3)

\left [ -5,1 \right ] \cup \left [ 3,\infty \right)

Incorrect option

Option 4)

None of these. 

Incorrect option

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