## pokemon23 3 years ago I need help with my math hw solving quadratic equations can someone help me understand it by helping guide me through I will surely appreciated the effort I'm here to learn :D

1. pokemon23

The first question is $x ^{2} -3x +2=0$

2. sonicx28@sbcglobal.net

You can either inspect the quadratic equation to see what 2 numbers multiply to be +2 and add up to be -3. Then you can write rewrite the quadratic in terms of two factors (x-2)(x-1) = 0 then by the zero product property if one of the factors is zero then the whole thing is zero so you can then solve the equations: x -2 =0 and x-1 = 0 and soon enough you'll find that x=2 and x=1 are the roots to the quadtratic.

3. sonicx28@sbcglobal.net

Another approach is to use the quadratic formula which is a sure-fire way of finding the roots but the catch is that it must be in the standard form which is $y = ax^2 + bx + c$ and then you would use the quadratic formula: $x = {-b \pm \sqrt(b^2-4ac) \over 2a}$ the $\sqrt(b^2-4ac)$ term is called the "discriminant" because if you get a negative number in that part of the equation then there are no real solutions and thus "discriminates" between real and imaginary solutions. Note that a quadratic equation has 2 roots...either both real or one real and one imaginary.

4. marshallinwashington

Sonic, I believe imaginary numbers come in pairs. So you have either two real roots or two imaginary roots.

5. sonicx28@sbcglobal.net

Another method you can use to solve quadratic equations is called "completing the square" which requires the coefficient of the $x ^2$ term to be one. The basic process involves you taking the b coefficient in $x^2 +bx+c$ and then dividing by 2 it and then squaring it and then plugging it back into the equation which will give us:$(x^2 + bx +({b \over 2})^2 ) - ({b \over 2})^2 + c = 0$. You put that $-({b \over 2})^2$ to maintain equality in the equation. It then follows that The first part in parenthesis is $x^2 + bx + ({b \over 2})^2 = (x+ ({b \over 2}))^2$. You can now have$(x + ({b \over 2}))^2 -({b \over 2})^2 + c = 0$ Then you would find the roots by solving for x by moving all the terms other than the perfect square to the other side then taking the square root of both sides and finally solving for x - remember when you take the square root of something you have to put a plus minus there. I hope that was of help.