Determine p if the following equation has equal roots: (p-3)xsquare + 4(p-3)x + 4 = 0

A quadratic equation has equal roots if and only if the determinant

equals zero.

In this case,

So, the determinant is

Expand the square and multiply terms to get

Which finally simplifies to

This expression equals zero if one of the factors equals zero:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right