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  • Help me answer: - If both the roots of the quadratic equation are real and sistinct and they lie in the interval [1, - Complex numbers and quadratic equations - JEE Main

If both the roots of the quadratic equation x^{2}-mx+4=0 are real and sistinct and they  lie in the interval [1,5], then m lies in the interval:

  • Option 1)

     

    (-5,-4)

  • Option 2)

     

    (5,6)

  • Option 3)

     

    (3,4)

  • Option 4)

     

    (4,5)

Answers (1)

best_answer

 

Condition for Real and distinct roots of Quadratic Equation -

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

- wherein

ax^{2}+bx+c= 0

is the quadratic equation

 

Given the quadratic equation 

x^2 - mx + 4 = 0 and root  \alpha,\beta\in[1,5]

Since roots are real and distinct from the concept 

(1) D > 0 \Rightarrow m^2 -16 > 0 \Rightarrow m\in(-\infty, -4)\cup (4,\infty)

(2) f(1)\geq 0 \Rightarrow 5 - m\geq 0\Rightarrow m\in (-\infty, 5]

(3) f(5)\geq 0 \Rightarrow 29 - 5m\geq 0 \Rightarrow m\in(-\infty, \frac{29}{5})

(4) 1 < \frac{-b}{2a} < 5 \Rightarrow 1 < \frac{m}{2} < 5 \Rightarrow m\in (2,10)

\Rightarrow m\in (4,5)


Option 1)

 

(-5,-4)

Option 2)

 

(5,6)

Option 3)

 

(3,4)

Option 4)

 

(4,5)
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