My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

Heres the question:

given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

Any help appreciated

Printable View

- Jan 9th 2009, 08:54 AMnickboiI'm not sure what this topic is called?
My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

Heres the question:

given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

Any help appreciated - Jan 9th 2009, 09:04 AMmasters
Hello nickboi,

This exercise has to do with "completing the square". With a quadratic and linear term given, what constant would you have to add in order for that to become a perfect square trinomial. Then, your perfect square trinomial becomes a binomial squared. - Jan 9th 2009, 09:08 AMnickboi
Thanks for the help. But im not quite sure what you mean by "Then, your perfect square trinomial becomes a binomial squared."

- Jan 9th 2009, 09:11 AMHallsofIvy
Go ahead and multiply out the right side:

In order that those be the same for all x, you must have the same coefficients: -14= 2b and a= b^2.

As masters said, that is basically "completing the square". - Jan 9th 2009, 09:19 AMnickboi
Thanks you two, i'll give that a try and post my success.

- Jan 9th 2009, 09:24 AMnickboi
It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.

- Jan 9th 2009, 09:35 AMmasters