Question

Find the value of p so that the equation 3x^-5x-2p=0 has equal roots also find the roots

Answer 1

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 $\frac{-b}{2a}$.

• Root of the equation is $\frac{5}{6}$.

Answer 2

A=3. B=5 C=2p

D=B SQUARE - 4 AC

= 5 ×5 - 4×3×2P

=25 - 24P

24P=25

P= 25/24