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JEE Main20257 Apr 2025Morning ShiftMathematicsQuadratic EquationActual

Let the set of all values of p R , for which both the roots of the equation x^2-(p+2) x+(2 p+9)=0 are negative real numbers, be the interval ( , ] . Then -2 is equal to

Options

  1. A0
  2. B9
  3. C5
  4. D20

Correct answer

C. 5

Step-by-step solution

Using location of roots : (i) D 0 (ii) - b 2 a 0 (iii) a. f (0) 0 aligned & (p+2)^2-4(2 p+9) 0 & (p+4)(p-8) 0 p+2 0 2 p+9 0 aligned Intersection p (- 9 2 ,-4 ] -2 =-4+9=5

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