Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 12/x=3
-
Equation x^3=3
-
Equation 7x-4=x-16
-
Equation sin^24𝑥−sin4𝑥−2=0
- Express {x} in terms of y where:
- -6*x-11*y=-20
- -15*x+7*y=1
- -1*x-20*y=1
- -1*x-15*y=13
-
Identical expressions
- x^ two - four *x- sixty = zero
- x squared minus 4 multiply by x minus 60 equally 0
- x to the power of two minus four multiply by x minus sixty equally zero
- x2-4*x-60=0
- x²-4*x-60=0
- x to the power of 2-4*x-60=0
- x^2-4x-60=0
- x2-4x-60=0
- x^2-4*x-60=O
-
Similar expressions
- x^2-4*x+60=0
- x^2+4*x-60=0
x^2-4*x-60=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
$$a = 1$$
$$b = -4$$
$$c = -60$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = -6$$
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
$$a = 1$$
$$b = -4$$
$$c = -60$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (-60) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -60$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -60$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -60$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -60$$
Sum and product of roots
[src]
sum
-6 + 10
$$-6 + 10$$
=
4
$$4$$
product
-6*10
$$- 60$$
=
-60
$$-60$$
-60