Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x=18-x
-
Equation x^4=(2*x-3)^2
-
Equation 9*x^2=54*x
-
Equation cos(x)+sin(x)=0
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 7*x-2*y=20
- -1*x-20*y=-17
- 9*x+18*y=3
- Graphing y =:
- x^2+3x-28
-
Identical expressions
- x^ two +3x- twenty-eight = zero
- x squared plus 3x minus 28 equally 0
- x to the power of two plus 3x minus twenty minus eight equally zero
- x2+3x-28=0
- x²+3x-28=0
- x to the power of 2+3x-28=0
- x^2+3x-28=O
-
Similar expressions
- x^2-3x-28=0
- x^2+3x+28=0
x^2+3x-28=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = 3$$
$$c = -28$$
, then
$$D = b^2 - 4\ a\ c = $$
$$3^{2} - 1 \cdot 4 \left(-28\right) = 121$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -7$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = 3$$
$$c = -28$$
, then
$$D = b^2 - 4\ a\ c = $$
$$3^{2} - 1 \cdot 4 \left(-28\right) = 121$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -7$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -28$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -28$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -28$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -28$$
Sum and product of roots
[src]
sum
-7 + 4
$$\left(-7\right) + \left(4\right)$$
=
-3
$$-3$$
product
-7 * 4
$$\left(-7\right) * \left(4\right)$$
=
-28
$$-28$$
The graph