Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+3x+2=0
-
Equation z^2-6*z+10=0
-
Equation x^2+5x+6=0
-
Equation -x/7+x=15/7
- Express {x} in terms of y where:
- -20*x-6*y=4
- -13*x+7*y=-15
- 5*x-14*y=-15
- -12*x-10*y=-16
-
Identical expressions
- x^ two - four *x+ eight + two - three *x= zero
- x squared minus 4 multiply by x plus 8 plus 2 minus 3 multiply by x equally 0
- x to the power of two minus four multiply by x plus eight plus two minus three multiply by x equally zero
- x2-4*x+8+2-3*x=0
- x²-4*x+8+2-3*x=0
- x to the power of 2-4*x+8+2-3*x=0
- x^2-4x+8+2-3x=0
- x2-4x+8+2-3x=0
- x^2-4*x+8+2-3*x=O
-
Similar expressions
- x^2-4*x+8+2+3*x=0
- x^2-4*x-8+2-3*x=0
- x^2+4*x+8+2-3*x=0
- x^2-4*x+8-2-3*x=0
x^2-4*x+8+2-3*x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = 10$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 10 + \left(-7\right)^{2} = 9$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 2$$
Simplify
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = 10$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 10 + \left(-7\right)^{2} = 9$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 2$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 10$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 10$$
Sum and product of roots
[src]
sum
2 + 5
$$\left(2\right) + \left(5\right)$$
=
7
$$7$$
product
2 * 5
$$\left(2\right) * \left(5\right)$$
=
10
$$10$$
The graph