help

sometimes300 · #1 $Old$ January 11th, 2009, 06:01 AM

I'm doing a practice test we received for hw. It has been a while since I have taken a math class and the prof says this is supposed to be a refresher for us. But these three problems seem like a foreign language. I am having a hard time remembering how to do some of the problems.If you can point me in the right direction would help out, thanks

9. Determine the constant that should be added to the binomial so that it becomes a perfect - square trinomial. Then write and factor the trinomial.

x2( x is squared ) + 1 over 6 (fraction) an x is next to the fraction

10. Solve 7x2( squared ) + 10x + 2 = 0

11. Solve x2(squared) + 14x + 38 = 0

running-gag · #2 $Old$ January 11th, 2009, 06:23 AM

Quote:

Originally Posted by sometimes300 $View Post$

I'm doing a practice test we received for hw. It has been a while since I have taken a math class and the prof says this is supposed to be a refresher for us. But these three problems seem like a foreign language. I am having a hard time remembering how to do some of the problems.If you can point me in the right direction would help out, thanks

9. Determine the constant that should be added to the binomial so that it becomes a perfect - square trinomial. Then write and factor the trinomial.

x2( x is squared ) + 1 over 6 (fraction) an x is next to the fraction

10. Solve 7x2( squared ) + 10x + 2 = 0

11. Solve x2(squared) + 14x + 38 = 0

Hi

9. You need to find $\alpha$ such as $x^2+\frac{1}{6}x+\alpha$ is a perfect square

You surely know the equality (x+y)²=x²+2xy+y²

Therefore $2y = \frac{1}{6}$ which leads to $y = \frac{1}{12}$

Then $y^2 = \frac{1}{144}$

$x^2+\frac{1}{6}x+\frac{1}{144} = (x + \frac{1}{12})^2$

For the next exercises you have to know how to solve equations like $a x^2 + b x + c =0$

If there are no evident solution then you calculate the discriminant $\Delta = b^2 - 4 a c$

If $\Delta < 0$ then there are no real solutions
Otherwise the solution(s) are given by the following formula

$x_1 = \frac{-b - \sqrt{\Delta}}{2 a}$

$x_2 = \frac{-b + \sqrt{\Delta}}{2 a}$

skeeter · #3 $Old$ January 11th, 2009, 06:25 AM

Quote:

Originally Posted by sometimes300 $View Post$

I'm doing a practice test we received for hw. It has been a while since I have taken a math class and the prof says this is supposed to be a refresher for us. But these three problems seem like a foreign language. I am having a hard time remembering how to do some of the problems.If you can point me in the right direction would help out, thanks

9. Determine the constant that should be added to the binomial so that it becomes a perfect - square trinomial. Then write and factor the trinomial.

x2( x is squared ) + 1 over 6 (fraction) an x is next to the fraction

10. Solve 7x2( squared ) + 10x + 2 = 0

11. Solve x2(squared) + 14x + 38 = 0

$x^2 + \frac{1}{6}x$

halve the linear coefficient, square, and add the result ...

$x^2 + \frac{1}{6}x + \left(\frac{1}{12}\right)^2$

factor the perfect square ...

$\left(x + \frac{1}{12}\right)^2$

$7x^2 + 10x + 2 = 0$

use the quadratic formula ... $a = 7$ , $b = 10$ , $c = 2$

$b^2-4ac = 10^2 - 4(7)(2) = 44$

$x = \frac{-10 \pm \sqrt{44}}{14} = \frac{-5 \pm \sqrt{11}}{7}$

another method (completing the square) ...

$x^2 + 14x + 38 = 0$

$x^2 + 14x = -38$

$x^2 + 14x + 49 = -38 + 49$

$(x + 7)^2 = 11$

$x + 7 = \pm \sqrt{11}$

$x = -7 \pm \sqrt{11}$