# Math

posted by .

how do you prove the quadratic equation?

• Math -

the proof is simply to complete the square for a generalised quadratic equation. Like this:
ax2(xsquared) + bx + c = 0
Take 'a' outside:
a[x2 + bx/a + c/a] = 0
Divide through by 'a':
x2 + bx/a + c/a = 0
Complete the square:
(x + b/2a)2 - b2/4a2 + c/a = 0
Rearrange to find x:
(x + b/2a)2 = b2/4a2 - c/a
x + b/2a = (+/-)sqrt[b2/4a2 - c/a]
x = -b/2a (+/-) sqrt[b2/4a2 - c/a]
Finally, fiddle around so that (1/2a) can be taken out as a common factor:
x = -b/2a (+/-) sqrt[b2/4a2 - 4ac/4a2]
x = -b/2a (+/-) sqrt[(1/4a2)(b2 - 4ac)]
x = -b/2a (+/-) sqrt(1/4a2)sqrt(b2 - 4ac)
x = -b/2a (+/-) (1/2a)sqrt(b2 - 4ac)
x = [ -b (+/-) sqrt(b2 - 4ac) ] / 2a.

• Math -

a bit easier to read ....

divide by a

x^2 + (b/a)x = -c/a
complete the square , add b^2/(2a^2) to both sides

x^2 + (b/a)x + b^2/(4a^2) = b^2/(4a^2) - c/a
write the left side as a square and add the two terms on the right
(x + b/(2a) )^2 = (b^2 - 4ac)/(4a^2)
take √ of both sides

x + b/(2a) = ± √(b^2 - 4ac)/(2a)
x = -b/(2a) ± √(b^2 - 4ac)/(2a)
= (-b ± √(b^2 - 4ac)/(2a)

## Similar Questions

1. ### algebra II

I'm quite clueless as to how to solve this. I know the quadratic equation but am not sure how to get this equation into the format to plug in to the quadratic... Solve the quadratic equation using the formula [1/(1+x)]-[1/(3-x)]=(6/35) …
2. ### College Math : Linear Algebra

Suppose A is a square matrix satisfying the equation A^3 - 2I = 0. Prove that A and (A - I) respectively are invertible. (the hint is to find an explicit equation for A^-1. To prove A is invertible, this is what I did although I don't …
3. ### maths

If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m:n prove that mnb^2=(m+n)^2 ac
4. ### maths

If the sum of the squares of the roots of the quadratic equation ax^2 + bx + c = 0 is m:n, prove that b^2= 2ac + 4a^2 I really have no idea how to prove it so pls help
5. ### Math

I can't remember how you find the roots of quadratic equations other than determining the zeroes of the equation and finding the x-intercepts. Can someone please give me a clear answer on this as my dad has been useless on this topic …
6. ### math

Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?
7. ### math help how do i do this

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring. −b b^2 − 4ac 2a Use the part of the quadratic formula that you chose above and find its value, given the following …
8. ### math help plsss plsss

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring. −b b^2 − 4ac 2a Use the part of the quadratic formula that you chose above and find its value, given the following …