Roots of a Quadratic Equation

Question

The derivative of the quadratic formula is both values of x, which are obtained by addressing the quadratic equation. These derivatives of a quadratic equation are also called absolute nos of the formula. For example, the roots of the formula x2 - 3x - 4 = 0 are x = -1 and x = four because each satisfies the formula. that is,

At x = -1, (-1 )2 - 3( -1) - 4 = 1 + 3 - 4 = 0

At x = 4, (4 )2 - 3( 4) - 4 = 16 - 12 - 4 = 0

There are different methods for finding the derivative of a quadratic equation. The use of the quadratic formula calculator is one of them.

Ashish Gupta · Answer

Roots of quadratic equations are TWO values of `x ` ,If a quadratic equation can be factored, the roots of the equation can be found using the factors.

Margarita Donkoh Lockner · Answer

Hi Robert, I would like to help you!Yes, that's right! The use of the quadratic formula is one of the ways to find the roots of a quadratic equation. This formula is the following: where a, b and c are taken from: Hence, for your example, a=1, b=-3 and c=4.Once you have put these in the quation, your answers for x are 4 and -1

Ashish Patel · Answer

The quadratic formula can be used to solve quadratic equations that you are unable to factorise. Using the formula (-b ± sqrt(b^2 - 4ac)) / 2a. Where a quadratic is in the form ax^2 + bx + c = 0

substituting the values of a=1 b=-3 and c=-4

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

when simplified results in

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

Hence

x = (3 + 5) / 2 or x = (3 - 5) / 2

x = -1/4

Kum Nagul Nirosh · Answer

You can factorize the multiple of ‘ac’ in a standard quadratic equation as ax2+bx+c=0. So you can rewrite the equation as x2-4x+x-4=0, now you can factorize as (x+1)(x-4)=0You can also use standard quadratic solution equation as well which is,

Syed Taqveem Ali Mohsin · Answer

x = (-b ± √(b^2 - 4ac)) / (2a)

Fekadu Gebre · Answer

There are 3 methods to solve a quadratic equation, these areCompleting square methodFactorisationUsing the quadratic formulaHere let's use the factorisation method,The equation is x2-3x-4 = 0 So you have to find two numbers  their sum is -3( the coefficient of X) and their product is -4( That is the power of the leading coefficient, in this case the 1 multiplied by the constant, in this case -4, therefore 1*-4= -4) The two numbers are -4 and 1, because -4*1= -4  and -4+1= -3Therefore, the equation becomes (x-4 ) (x+1)=0so, x-4 =0 and x+1=0 x= 4 and x=-1 therefore the solution is x= 4 and x=-1

Delia Munteanu · Answer

Hope this was helpful.

Aryaman · Answer

The second method is to find a same pair of numbers which add together to get the middle number in the quadratic equation which in the example is -3 and that same pair of numbers that multiply to get the 3rd number which is -4. This pair of numbers are the solution which is -4 and 1. Then equate both of these to 0 using x.x-4=0   and x+1=0 ,,  then the final values for x is 4 and -1. These are the roots of the quadratic equation.

Scott Magee · Answer

The “roots” of a quadratic formula are essentially the X-Intercepts of a graph i.e. where does a graph cross the X-axis. Some quadratics will have two roots, some only one and some will have zero. A useful tool to know which category a quadratic falls into is to first use the discriminant which is b^2 - 4ac where a,b and c are the coefficients of ax^2 + box + c = 0 respectively. If the discriminant is positive there are two roots, if it is equal to zero then there is one root and if it is less than zero there are no real roots. Once you know this you can either solve by factorising your quadratic which would involve taking out a common factor, or a difference of two squares or by solving a trinomial or any combination of these. Alternatively the quadratic formula could be used which can obtain the roots of any quadratic and it is given by x = [-b +- SQRT(b^2 - 4ac) ] / 2a or an online calculator could also be used!

Eshal Aamir · Answer

To find how many roots of a quadratic formula there are use the part of the quadratic formula known as the derivative. This is root b^2 -4ac. If the answer to that is less than 0 then there is no real roots, if the answer is exactly 0, there is 1 real root. If the answer is more than 0 then there are 2 real roots.

James Hilder · Answer

I agree with Muhammed above. The easiest way is to use the formula. But you may be asked to factorize it too, if it can be factorized. Or by graph-the roots or solutions are where the curve crosses the y-axis.

Purushotam Kumar · Answer

you  can solve it be discriminant method

Muhammed Abulkasem · Answer

The roots of a quadratic equation ax2 + bx + c = 0 can be found using the quadratic formula that says x = (-b ± √ (b2 - 4ac)) /2a.