Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (5x+2)(-x-4)=0
-
Equation sin(x)=3/4
-
Equation 9-2*(-4*x+7)=7
-
Equation x^2-4x+5=0
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-4*y=-20
- 4*x-7*y=4
- -6*x-12*y=9
- Derivative of:
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x^2+2x-3
- Integral of d{x}:
-
x^2+2x-3
- Canonical form:
- x^2+2x-3
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Identical expressions
- x^ two +2x- three
- x squared plus 2x minus 3
- x to the power of two plus 2x minus three
- x2+2x-3
- x²+2x-3
- x to the power of 2+2x-3
-
Similar expressions
- x^2-2x-3
- x^2+2x+3
x^2+2x-3 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
$$a = 1$$
$$b = 2$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
Simplify
$$x_{2} = -3$$
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 - it is the discriminant.
Because
$$a = 1$$
$$b = 2$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (-3) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
Simplify
$$x_{2} = -3$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -3$$
Sum and product of roots
[src]
sum
0 - 3 + 1
$$\left(-3 + 0\right) + 1$$
=
-2
$$-2$$
product
1*-3*1
$$1 \left(-3\right) 1$$
=
-3
$$-3$$
-3
The graph