maths help please?

Question

this is the question:

given that for all values of x:

3x^2-12x+4=m(x+p)^2+n

(^2 means to the power of 2)

find the values of m,p and n

i don't understand it....?

ten points to whoever can help

Answer 1

3(x^2-4x+4)-8=3(x-2)^2-8
so
m=3
p=-2
n=-8

Answer 2

This is an identity.

3x^2 - 12x + 4 = m(x + p)^2 + n

3x^2 - 12x + 4 = m(x^2 + 2px + p^2) + n

3x^2 - 12x + 4 = mx^2 + 2pmx + (mp^2 + n)

As this is an identity so the coefficients of 'x^2', coefficients of 'x' and terms independent of 'x' in both sides will be equal.

coefficients of 'x^2': 3 = m

coefficients of 'x^2': -12 = 2pm or pm = -6

terms independent of 'x': 4 = mp^2 + n

Thus we have 3 equations and 3 unknowns, m,n,p.

m = 3 _________(1)
pm = -6 _______(2)
mp^2 + n = 4 _______(3)

Substituting 'm' from (1) in (2), p = -2

Substituting m = 3 and p = -2 in (3), n = -8

Thus, m = 3, n = -8, p = -2

Answer 3

Completing the squares method is required here to change 3x^2-12x+4 to the format given.

3x^2 - 12x + 4
= 3(x^2 - 4x + 4/3)
= 3[(x-2)^2 -2 2/3]
= 3(x-2)^2 - 8

So m=3, p=-2 and n=-8

Answer 4

For x = 1 -5 = m(1+p)^2 + n equation 1
For x = 2 -8 = m(2+p)^2 + n equation 2
For x = 3 -14 = m(3+p)^2 + n equation 3

Solve in matrix form

Answer 5

Complete the square!

I can tell you straight off that m=3 and p=2. Find n from the process.

Answer 6

This means:
m(x+p)(x+p)+n = m(x^2+2px+p^2)+n

= mx^2 + 2mpx + mp^2 + n

so,
m = 3
2mp = -12
mp^2+n = 4

Solve the rest from there.

Answer 7

I've tried to solve it, but I got stuck! You obviously have some crazy maths teacher!! I'm not quite sure how old you are but this is pretty much complicated!!!

Answer 8

MAKE IT YOUR OWN...