Question

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

Answer 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:

Answer 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