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  • I have a doubt, kindly clarify. - Consider the quadratic equation Let S be the set of all integral values of c for which one root of - Complex numbers and quadratic equations - JEE Main

Consider the quadratic equation (c-5)x^{2}-2cx+(c-4) = 0,c\neq 5. Let S be the set of all integral values of c for which  one root of the equation lies in the  interval (0,2) and its other root lies in the interval (2,3). Then the number of the element in S is::

  • Option 1)

     

    18

  • Option 2)

     

    12

  • Option 3)

     

    10

  • Option 4)

     

    11

Answers (1)

best_answer

 

Quadratic Expression -

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

- wherein

a\neq 0

a,b,c\in R,\: \:

 

Given quadratic equation is,

 

Let, f(x) = \left ( c - 5 \right ) x^{2} - 2cx + c - 5

From the concept,

f(0) . f(2) < 0 ...... (1)

and f(2) . f(3) < 0 ...... (2)

From (1) and (2)

(c-5) (c-24) < 0

and (c-24) (4c-49) < 0

\Rightarrow \frac{49}{4} < c < 24

\therefore s = \left \{ 13, 14 , 15 .....\left. 23 \right \} \right.

 


Option 1)

 

18

Option 2)

 

12

Option 3)

 

10

Option 4)

 

11
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