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AS algebra question,solve a and b. help?
just finished my GCSE's, doing homework preparation for AS.
Given that
x squared-14x+a= ((x+b)squared) for all values of x,
find the value of a and b
I completely forgot how to do this.. help!
thanks!
2 Answers
- ?Lv 79 years agoFavorite Answer
x^2-14x+a=(x+b)^2 for all x=>
x^2-14x+a=x^2+2bx+b^2=>
2b=-14=>
b=-7
a=b^2=>
a=(-7)^2=>
a=49
- Jim HLv 59 years ago
x^2-14x+a = (x+b)^2
x^2-14x+a = (x+b)(x+b) = x^2+2bx+b^2
Subtract x^2 from both sides leaves you with:
-14x+a = 2bx + b^2
For this to be true for all values of x, -14x = 2bx
Divide both sides by 2x gives b = -7
substitute this back into the equation: -14x + a = 2(-7)x + (-7)^2
-14x+a = -14x + 49, so a = 49
a = 49, b = -7
