Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2+5*x-6=0
-
Equation x+4=0
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Equation x^2+6x+9=0
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Equation (x-2)^5+(4-x)^5=2
- Express {x} in terms of y where:
- 18*x+12*y=18
- -20*x-13*y=15
- 12*x-3*y=-2
- 17*x+1*y=-11
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Identical expressions
- x^ two +x- thirty = zero
- x squared plus x minus 30 equally 0
- x to the power of two plus x minus thirty equally zero
- x2+x-30=0
- x²+x-30=0
- x to the power of 2+x-30=0
- x^2+x-30=O
-
Similar expressions
- x^2-x-30=0
- x^2+x+30=0
x^2+x-30=0 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
$$a = 1$$
$$b = 1$$
$$c = -30$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -6$$
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
$$a = 1$$
$$b = 1$$
$$c = -30$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-30) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -30$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -30$$
Sum and product of roots
[src]
sum
-6 + 5
$$-6 + 5$$
=
-1
$$-1$$
product
-6*5
$$- 30$$
=
-30
$$-30$$
-30
The graph