Polynomials question (1 Viewer)

[Mr. Osama]

i put the 2 questions on word document...can someonce plz post up how to do em.

 

[Trefoil]

a.) a(x-1)2 +b(x-1)+c º x2
Answer: expand and equate
ax^b-2ax+a+bx-b+c=x^2
a=1
x^b-2x+1+bx-b+c=x^2
-2+b=0
b=2
-1+c=0
c=1

Solution set:
{a=1
{b=2
{c=1

b.) a(x+2) 2 + b(x+3) 2 + c(x +4) 2 º 2x2 + 8x +6
answer the same:
a(x+2) 2 + b(x+3) 2 + c(x +4) 2 º 2x2 + 8x +6
ax^2+4ax+4a+bx^2+6bx+9b+cx^2+8cx^2+16c=2x^2+8x+6
x^2(a+b+c) + x(4a+6b+8c) + (4a+9b+16c) = 2x^2+8x+6
1) 2=a+b+c
2) 8=4a+6b+8c
3) 6=4a+9b+16c

2)-3):
4) 2=-3b-8c -> 4)' -2=3b+8c
2)-4*1):
5)0=b+2c -> 5)' 0=4b+8c
5)'-4)':
2=b
Substitute:
c=-1
a=1

Solution set:
{a=1
{b=2
{c=-1

EDIT: I have corrected the c value for the first question.

 

[Mr. Osama]

a.) a(x-1)2 +b(x-1)+c º x2
Answer: expand and equate
ax^b-2ax+a+bx-b+c=x^2
a=1
x^b-2x+1+bx-b+c=x^2
-2+b=0
b=2
2+c=0
c=-2
Solution set:
{b=2
{c=-2


a(x+2) 2 + b(x+3) 2 + c(x +4) 2 º 2x2 + 8x +6
ax^2+4ax+4a+bx^2+6bx+9b+cx^2+8cx^2+16c=2x^2+8x+6
x^2(a+b+c) + x(4a+6b+8c) + (4a+9b+16c) = 2x^2+8x+6
1) 2=a+b+c
2) 8=4a+6b+8c
3) 6=4a+9b+16c

2)-3):
4) 2=-3b-8c -> 4)' -2=3b+8c
2)-4*1):
5)0=b+2c -> 5)' 0=4b+8c
5)'-4)':

what does that dot on top of the two mean.

 

[Trefoil]

The small zero was an identity sign in the word document.

 

[FinalFantasy]

a.) a(x-1)2 +b(x-1)+c º x2
Answer: expand and equate
ax^b-2ax+a+bx-b+c=x^2
a=1
x^b-2x+1+bx-b+c=x^2
-2+b=0
b=2
2+c=0
c=-2
Solution set:
{b=2
{c=-2

isn't it a-b+c=0 so 1-2+c=0 so c=1

 

[~ ReNcH ~]

My working for a):

a(x-1)² + b(x-1) + c = x²
.'. ax² - 2ax + a +bx - b +c = x²
.'. ax² - (2a-b)x + (a-b+c) = x²
Equating coefficients:
a=1
2a - b = 0 --> b=2
a - b + c = 0 --> c=1

.'. a=1, b=2, c=1