Polynomials (1 Viewer)

[shaon0]

Find constants a,b,c such that:
x^2 +10x+c = a (x+2)^2 + b(x+1)

 

[undalay]

Equate like terms:

x^2 = ax^2
a = 1

10x = 4ax + bx
10 = 4 +b
b=6

c = 4a +b
c = 4 + 6
c = 10

 

[shaon0]

Equate like terms:

x^2 = ax^2
a = 1

10x = 4ax + bx
10 = 4 +b
b=6

c = 4a +b
c = 4 + 6
c = 10

Thanks

 

[shaon0]

sorry, i have another question:
Write (2-x)/(x+2)(x-1) in the form a/(x+2) + b/(x-1)

 

[tacogym27101990]

sorry, i have another question:
Write (2-x)/(x+2)(x-1) in the form a/(x+2) + b/(x-1)

multiply both sides by (x+2)(x-2)

sode then you get:
2-x = a(x-1) + b(x+2)

and equate the coefficient of x and the constants

you get 2= 2b -a (1)
and......-1=a+b (2)
(1)+(2)

1=3b b= 1/3, a =-4/3

 

[shaon0]

multiply both sides by (x+2)(x-2)

sode then you get:
2-x = a(x-1) + b(x+2)

and equate the coefficient of x and the constants

you get 2= 2b -a (1)
and......-1=a+b (2)
(1)+(2)

1=3b b= 1/3, a =-4/3

cool, i got the equating part right.