Question

find value of p for which quadretic equation x2-px+p+3=0 have one root positive and one root negative​

Answer 1

Answer:

Any p < -3.

Step-by-step explanation:

To have a positive root and a negative root we need the product of the roots to be negative.

The product of the roots is given by the constant coefficient, which here is p+3.  So we need p + 3 < 0 ; that is

  p < -3.

We really should check that the roots are real, too.  This corresponds to the discriminant being non-negative.  The discriminant here is

 p² - 4 ( p + 3 ) = p² - 4p - 12 = ( p + 2 ) ( p - 6 )

and this certainly is positive when p < -3, so we're okay.

Conclusion, whenever p < -3, the quadratic has two real roots, one negative and one positive.

Hope this helps!