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

Question

pokemon23 · Answer

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

anonymous · Answer

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.

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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.