find the values of
p for which
the equation 3x² – 5x – 2p = 0
has real neal roots​

2 thoughts on “find the values of<br />p for which<br />the equation 3x² – 5x – 2p = 0<br />has real neal roots​”

1. Answer:

   The value of p so that the equation 3x²-5x-2p=0 has equal roots is -25/24 and the root is 5/6.

   Given equation is 3x²-5x-2p=0.

   We have to find the value of p so that the equation has equal roots.

   For a quadratic equation to have equal roots b²-4ac should be equal to zero in the quadratic equation ax²+bx+c=0.

   Now comparing the equation with the standard equation ax²+bx+c=0 , we get

   a=3 , b=-5 , c=-2p

   Now, b²-4ac = 0 as the equation has equal roots

   (-5)²-4(3)(-2p)=0

   25+24p=0

   p = -25/24

   Now the quadratic equation becomes 3x²-5x+25/12=0.

   Root of the equation is .

   Root of the equation is .

   Step-by-step explanation:

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2. Given equation is 3x² – 5x – 2p = 0

   Comparing with standard quadratic equation

   ax² + bx + c = 0 we get

   a = 3 , b = -5 , c= 2p

   for real root

   b² – 4ac > 0

   (5)² – 4(3)(2p) > 0

   25 – 24p >0

   p > 25/24

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