How do you solve quadratic equations?

Quadratic equations have the form ax^2 + bx + c = 0, where a, b, and c are rational coefficients.

For example, in the equation 8x^2 + 2x - 3 = 0, a = 8, b = 2, and c = -3.

What you need to do is factor the equation, because when factored, to equal zero, either one or the other factors is equal to zero. These values of x are the places where the parabolic function described by this equation crosses the x-axis.

For example, x^2 + 4x + 3 factors to (x + 1)(x + 3). If x^2 + 4x + 3 = 0, then either x + 1 or x + 3 = 0, so x = -1 or x = -3. If you draw that curve that equation describes, it will cross the x-axis at x = -1 or x = -3.

Another easy one looks like (sx)^2 - t^2 = 0, such as 9x^2 - 4.

(sx)^2 - t^2 = (sx + t)(sx - t), so 9x^2 - 4 = (3x + 2)(3x - 2).

Let's go back to our first equation, 8x^2 + 2x - 3 = 0, where a = 8, b = 2, and c = -3. There is something called the Quadratic Formula that can be used to solve these, when the solution is not obvious.

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

Here

x = (-2 +/- sqrt(2^2 - 4 * 8 * -3)) / (2 * 8)

x = (-2 +/- sqrt(4 + 96)) / 16

x = (-2 +/- sqrt(100)) / 16

x = (-2 +/- 10) / 16

x = 8/16 or x = -12/16

x = 1/2 or x = -3/4

So the factors of 8x^2 + 2x - 3 are

(4x + 3)(2x - 1)

One other important thing to know is that the term inside the radical, b^2 - 4ac is called the discriminant. Analyzing it can tell you a lot about the equation before you find its solutions.

If b^2 - 4ac > 0, there are two real roots.

If b^2 - 4ac > 0 and is a square, there are two rational roots.

If b^2 - 4ac = 0, then there are two identical rational roots.

If b^2 - 4ac < 0, then the roots are imaginary.

I hope this helps. PM me if you have any questions. I applaud your curiosity.

it depends upon what you are solving for:

usually when solving for Quadratic Equations, you are given a y value to find two, one or no x values

they also usually contain at least one x value to a power (X^2) for example

the standard equation is Y = ax^2 + bx + c

to solve for Y, you should use the quadratic equation rule and simply substituting in the values, but only once the formula is equal to zero

x = (-b ± SQRT(b^2 - 4ac))/2a

e.g

Y = x^2 + 9

if Y = 10

10 = 1x^2 + 9

10 - 10 = 1x^2 + 9 - 10 (subtract 10 from each size)

0 = 1x^2 + -1

as you can see I have used a simple formula

x = (-b ± SQRT(b^2 - 4ac)/2a

x = (-0 ± SQRT(0^2 - 4*1*-1))/2*1

x = (0 ± SQRT(-4))/2

x = (0 + 2)/2 or (0 - 2)/2

x = 1 or -1

You can also find only one point:

Y = x^2 +10

if Y = 10

10 = 1x^2 + 10

10 - 10 = 1x^2 + 10 - 10 (subtract 10 from each size)

0 = 1x^2

as you can see I have used a simple formula

x = (-b ± SQRT(b^2 - 4ac)/2a

x = (-0 ± SQRT(0^2 - 4*1*0))/2*1

x = (0 ± SQRT(0))/2

x = (0 + 0)/2 or (0 - 0)/2

x = 0 or 0

as you can see, if the SQRT part is equal to zero, then the entire equation becomes equal to -b

in this case because be is equal to zero, the only possible x-value is zero

You can also find no points:

Y = x^2 +11

if Y = 10

10 = 1x^2 + 11

10 - 10 = 1x^2 + 11 - 10 (subtract 10 from each size)

0 = 1x^2 + 1

as you can see I have used a simple formula

x = (-b ± SQRT(b^2 - 4ac)/2a

x = (-0 ± SQRT(0^2 - 4*1*1))/2*1

x = (0 ± SQRT(-4))/2 (this is where is becomes impossible)

trying to find the SQRT of a negative number is impossible (unless you know maths C) as it part of the unreal number season.

e.g. you know how 2 squared is equal to 2*2 equal to 4

-2 squared is also equal to 4, -2*-2 = 4 (negative * negative = positive)

when squaring a number you multiply the exact same number against its self and the result of squaring a number will always be a positive number so you can't (in the real number system) get the square root of a negative number

There is a simpler way, you could always use a graphing program and imput the equation equal to zero and then find the x intercepts. By the Way, you usually use quadratic equation to find x-intercepts anyway.

The amount of points you find is related to what the square rooted part is equal to:

0 < 2 points

0 = 1 point

0 > no points

Hi:

So you want to know quadratic equations here are some websites which can explain it better than I can here:

en.wikipedia.org/wiki/Quadratic_equation

www.mathsisfun.com/algebra/quadratic-equation.html

www.helpalgebra.com/articles/quadraticequations.htm

mathworld.wolfram.com/QuadraticEquation.html

www.purplemath.com/modules/quadform.htm

www.algebra.com/algebra/homework/quadratic - Cached

if you need more try this:

http://search.yahoo.com/search;_ylt=A0oG7t7A3ctPQ0...