Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5-2(x-1)=4-x
-
Equation x^2+x-4=0
-
Equation 2-3*(2*x+2)=5-4*x
-
Equation x^4=(4x-21)^2
- Express {x} in terms of y where:
- -10*x+16*y=-6
- 2*x+2*y=-6
- -17*x+13*y=-3
- -11*x-14*y=-3
-
Identical expressions
- x^ two -5x- fourteen = zero
- x squared minus 5x minus 14 equally 0
- x to the power of two minus 5x minus fourteen equally zero
- x2-5x-14=0
- x²-5x-14=0
- x to the power of 2-5x-14=0
- x^2-5x-14=O
-
Similar expressions
- x^2-5x+14=0
- x^2+5x-14=0
x^2-5x-14=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
$$a = 1$$
$$b = -5$$
$$c = -14$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -2$$
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
$$a = 1$$
$$b = -5$$
$$c = -14$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (-14) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -14$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = -14$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -14$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = -14$$
Sum and product of roots
[src]
sum
-2 + 7
$$-2 + 7$$
=
5
$$5$$
product
-2*7
$$- 14$$
=
-14
$$-14$$
-14
The graph