Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x+5=0
-
Equation 4*x^2-25=0
-
Equation x^2-x-7=0
- Express {x} in terms of y where:
- 14*x+3*y=-1
- -8*x-2*y=-11
- -12*x-19*y=-8
- 12*x-14*y=14
- Graphing y =:
- 5*x-x^2
- Derivative of:
- 5*x-x^2
- Factor polynomial:
- 5*x-x^2
-
Identical expressions
- five *x-x^ two
- 5 multiply by x minus x squared
- five multiply by x minus x to the power of two
- 5*x-x2
- 5*x-x²
- 5*x-x to the power of 2
- 5x-x^2
- 5x-x2
-
Similar expressions
- 5*x+x^2
5*x-x^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = -1$$
$$b = 5$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 5$$
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
$$a = -1$$
$$b = 5$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (-1) * (0) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 5$$
Vieta's Theorem
rewrite the equation
$$- x^{2} + 5 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 5 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 0$$
$$- x^{2} + 5 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 5 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 0$$