What are the values of ab and c in the quadratic equation 0=5x-4x^2-2

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How Does this Work?
Step by step solution :
Step 1 :
Step 2 :
Step 3 :
Solve Quadratic Equation using the Quadratic Formula
Two solutions were found :

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Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.

The name comes from "quad" meaning square, as the variable is squared (in other words x2).

These are all quadratic equations in disguise:

In disguise	In standard form	a, b and c
x2 = 3x -1	x2 - 3x + 1 = 0	a=1, b=-3, c=1
2(x2 - 2x) = 5	2x2 - 4x - 5 = 0	a=2, b=-4, c=-5
x(x-1) = 3	x2 - x - 3 = 0	a=1, b=-1, c=-3
5 + 1/x - 1/x2 = 0	5x2 + x - 1 = 0	a=5, b=1, c=-1

How Does this Work?

The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:

The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !

The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:

when it is positive, we get two real solutions,
when it is zero we get just ONE solution,
when it is negative we get complex solutions.

Learn more at Quadratic Equations

Note: you can still access the old version here.

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

0-(5*x-4*x^2-2)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

0 - ((5x - 22x2) - 2) = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 4x2-5x+2

The first term is, 4x2 its coefficient is 4 .

The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is +2

Step-1 : Multiply the coefficient of the first term by the constant 4 • 2 = 8

Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -5 .

-8	+	-1	=	-9
-4	+	-2	=	-6
-2	+	-4	=	-6
-1	+	-8	=	-9
1	+	8	=	9
2	+	4	=	6
4	+	2	=	6
8	+	1	=	9

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 2 :

4x2 - 5x + 2 = 0

Step 3 :

Parabola, Finding the Vertex :

3.1      Find the Vertex of   Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting "y" because the coefficient of the first term, 4 , is positive (greater than zero).Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 0.6250 Plugging into the parabola formula 0.6250 for x we can calculate the y -coordinate :
  y = 4.0 * 0.62 * 0.62 - 5.0 * 0.62 + 2.0
or   y = 0.438

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = 4x2-5x+2
Axis of Symmetry (dashed) {x}={ 0.62}
Vertex at {x,y} = { 0.62, 0.44} Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2 Solving 4x2-5x+2 = 0 by Completing The SquareDivide both sides of the equation by 4 to have 1 as the coefficient of the first term :
x2-(5/4)x+(1/2) = 0

Subtract 1/2 from both side of the equation :

x2-(5/4)x = -1/2

Now the clever bit: Take the coefficient of x , which is 5/4 , divide by two, giving 5/8 , and finally square it giving 25/64

Add 25/64 to both sides of the equation :

On the right hand side we have :

-1/2 + 25/64 The common denominator of the two fractions is 64 Adding (-32/64)+(25/64) gives -7/64

So adding to both sides we finally get :

x2-(5/4)x+(25/64) = -7/64

Adding 25/64 has completed the left hand side into a perfect square :

   x2-(5/4)x+(25/64)  =
   (x-(5/8)) • (x-(5/8))  =
  (x-(5/8))2 Things which are equal to the same thing are also equal to one another. Since

x2-(5/4)x+(25/64) = -7/64 and

x2-(5/4)x+(25/64) = (x-(5/8))2 then, according to the law of transitivity,

(x-(5/8))2 = -7/64

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(5/8))2 is

   (x-(5/8))2/2 =
  (x-(5/8))1 =
   x-(5/8)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(5/8) = √ -7/64

Add 5/8 to both sides to obtain:

x = 5/8 + √ -7/64
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1 Since a square root has two values, one positive and the other negative

x2 - (5/4)x + (1/2) = 0

has two solutions:

x = 5/8 + √ 7/64 • i

x = 5/8 - √ 7/64 • i

Note that √ 7/64 can be written as

√ 7 / √ 64 which is √ 7 / 8

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving 4x2-5x+2 = 0 by the Quadratic FormulaAccording to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC x = ———————— 2A

In our case, Accordingly, Applying the quadratic formula :

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)

Both i and -i are the square roots of minus 1

Accordingly,√ -7  =
                    √ 7 • (-1)  =
                    √ 7  • √ -1   =
                    ±  √ 7 • i

√ 7 , rounded to 4 decimal digits, is 2.6458
So now we are looking at:

x = ( 5 ± 2.646 i ) / 8

Two imaginary solutions :

x =(5+√-7)/8=(5+i√ 7 )/8= 0.6250+0.3307i or:
x =(5-√-7)/8=(5-i√ 7 )/8= 0.6250-0.3307i