Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
-
Equation x^2+8*x+15=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Derivative of:
-
(2x-1)²
-
Identical expressions
- (2x- one)²
- (2x minus 1)²
- (2x minus one)²
- 2x-1²
-
Similar expressions
- (2x+1)²
(2x-1)² equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(2 x - 1\right)^{2} = 0$$
We get the quadratic equation
$$4 x^{2} - 4 x + 1 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = -4$$
$$c = 1$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{1}{2}$$
$$\left(2 x - 1\right)^{2} = 0$$
We get the quadratic equation
$$4 x^{2} - 4 x + 1 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = -4$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (4) * (1) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --4/2/(4)
$$x_{1} = \frac{1}{2}$$
Sum and product of roots
[src]
sum
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
product
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2