Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^6=(3x-2)^3
-
Equation 2x^2+5x-2=0
-
Equation 1/4*x^2-4=0
-
Equation x^2-10x=0
- Express {x} in terms of y where:
- -14*x+12*y=-6
- -10*x+8*y=2
- -16*x+1*y=-14
- 4*x-1*y=12
- Factor polynomial:
- x^2+3*x-10
-
Identical expressions
- x^ two + three *x- ten = zero
- x squared plus 3 multiply by x minus 10 equally 0
- x to the power of two plus three multiply by x minus ten equally zero
- x2+3*x-10=0
- x²+3*x-10=0
- x to the power of 2+3*x-10=0
- x^2+3x-10=0
- x2+3x-10=0
- x^2+3*x-10=O
-
Similar expressions
- x^2+3*x+10=0
- x^2-3*x-10=0
x^2+3*x-10=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
$$a = 1$$
$$b = 3$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -5$$
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
$$a = 1$$
$$b = 3$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (1) * (-10) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -10$$
Sum and product of roots
[src]
sum
-5 + 2
$$-5 + 2$$
=
-3
$$-3$$
product
-5*2
$$- 10$$
=
-10
$$-10$$
-10
The graph