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To find roots of quadratic equation given as ax^2+bx+c=0, where a, b and c are coefficients and "a" is not equal to zero, there are different sets of conditions

Step 1- Determine discriminant, D= (b^2-4ac)

Step 2- Check, if D>0, then roots are real and equal,

              if D=0, then roots are real and distinct,

              if D<0, then roots are complex and conjugates

Step 3- find x1= -b +sqrt(D)/2a

Step4- find x2= -b-sqrt(D)/2a 

These are the roots.

A quadratic equation is any equation in the form ax2 + bx + c = 0 where a ≠ 0.  Any quadratic equation can be solved with the formula x = (-b +/-√(b2 - 4ac))/2a.   

Write your equation in the quadratic form. The official definition of a quadratic equation is a second-order polynomial equation expressed in a single variable, x, with a ≠ 0.[1] In simple terms, this just means that it's an equation with one variable (usually x) where the highest exponent of the variable is 2. In general terms, we can write this as ax2 + bx + c = 0

  • To get an equation in quadratic form, just get all of the terms on one side of the equals sign so that you have 0 on the other side. For example, if we want to get the equation 2x2 + 8x = -5x2 - 11 in quadratic form, we can do it like this:
  • 2x2 + 8x = -5x2 + 11
  • 2x2 + 5x2 + 8x = + 11
  • 2x2 + 5x2 + 8x - 11 = 0
  • 7x2 + 8x - 11 = 0 . Notice that this is in the standard ax2+ bx + c = 0 form mentioned above.

and then find the value of a, b, c and then apply the formula to find the value of x.

3 methods, the quadratic equation, factorise or complete the square

Factorisation and completing the square don't work for every quadratic but they will for most, if in doubt just use the equation.

Quadratic Equation:

x1 = -b + sqrt((b^2)-4ac)/2a

x2 = -b - sqrt((b^2)-4ac)/2a


Your quadratic will look like this, ax^2 + bx + c. Find 2 numbers which multiply to give c and add to give b. For example: x^2 + 5x + 6. 3*2 = 6 and 3+2 = 5 therefore x^2 + 5x +6 = (x+3)(x+2). The roots are the value of x that would make either bracket equal to 0, so in this case -3 (as -3 + 3 = 0) and -2. 

If your equation has a value of a that isn't 1 then factorising can be tricky, it is however doable, a good method is given here: http://http//www.purplemath.com/modules/factquad2.htm

Completing the square:


the formula for finding roots of a quadratic equation is

  1. -b+sqrt((b^2-4ac)/2a)
  2. -b-sqrt((b^2-4ac)/2a)

There are several options:

  • Factorising [ Putting them in to two pairs of brackets - e.g (x+2)(x+3)]
  • Completing the square
  • Quadratic formula
  • Sketching the graph

You can solve for x in a quadratic equation by factorising.

You can find roots of a quadratic equation ax^2+bx+c=0 simply sub in your values and your done!

well, you can find roots of a quadratic equation ax^2+bx+c=0 either by factorising or by using quadratic formula. Quadratic formula for finding roots :

x1 = (-b + sqrt(b*b-4*a*c)) / 2*a

x2 = (-b - sqrt(b*b-4*a*c)) / 2*a

This can be done by factorising or using the quadratic formula. Factorising is the easiest option but if the equation is not factorisable then the quad ration formula can also be used.

x1 = (-b + sqrt(b*b-4*a*c)) / (2*a)

x2 = (-b - sqrt(b*b-4*a*c)) / (2*a)

this solution are real when b*b-4*a*c >=0

ax^2+bx+c = 0, this is one standard form of quadratic equation, if you want to find the root of this quadratic equation, you can have two roots for this

root 1  =  -b+(square root of ((( b^2)-4ac)/2a)

root 2  =  -b-(square root of ((( b^2)-4ac)/2a)

If you have a quadratic equation, ax^2+bx+c, the roots are the numbers that make this equal to zero, which means you need to solve the equation ax^2+bx+c=0. The geometrical interpretation of this is that you find the coordinates of the points that your curve cuts the x-axis (because y=0). In some occasions it is easier to find the roots by factorising. Example: x^2-5x+6=0. We need two numbers that multiply to give 6 (the constant term) and add to give 5 (the coefficient of x). It is always easier to "guess" these numbers from their product. In our case these numbers are -3 and -2, because (-3)x(-2)=6 and -3-2=-5. Then your quadratic equation can be written in the form (x-3)(x-2)=0. A bracket times another bracket is equal to zero. This means that the first bracket is zero, so x-3=0 which means that x=3, or the other bracket is zero, so x-2=0 hence x=2. Hence your roots are x=2 and x=3. 

Unfortunately not all the quadratics are factorable. Why? Because in some occasions the roots are irrational numbers or fractions. In that case, we use the quadratic formula. Example x^2+x-1=0. It is quite clear that I cannot find two numbers that multiply out to give -1 and add up to +1. The formula is x=(-b+/-sqrt(b^2-4ac))/2a, so all you have to do is determine the values of a, b and c and substitute in the formula. a is the coefficient of x^2 (the number times by x^2). In our case, a=1. B is the coefficient of x (the number times by x). In our example, b=1, and c is the constant (the number without any x's, and in our case it is c=-1 (NEVER forget the signs).

When we substitute we get x=(-1+/-sqrt(1^2-4x1x(-1)))/2x1=(-1+/-sqrt5)/2

Thus, the first root will be (-1+sqrt5)/2 and the other (-1-sqrt5)/2.

I hope I did help :-)

The best method is to use the quadratic formula.

Given: ax^2+bx+c=0 is a quadratic equation .Then its roots are

root 1= (-b+square root of b^2-4ac)/2a

root 2=(-b-square root of b^2-4ac)/2a

hope it helps.

The roots of a function are the x intercepts.By definition the y coordinate of points lying on the x axis is 0.

therefore ,to find the root of a quadratic function ,we set

f(X) = 0 and solve the equation ax^2+bx+c=0

The roots of a function are the x intercepts.By definition the y coordinate of points lying on the x axis is 0.

therefore ,to find the root of a quadratic function ,we set

f(X) = 0 and solve the equation ax^2+bx+c=0

Use the formulae to find the roots of a quadratic equation.

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