Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1*(x-1)*(x-3)=0
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Equation x^2-11*x+30=0
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Equation -33-y=-19
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Equation x^2+7x=18
- Express {x} in terms of y where:
- -2*x-19*y=3
- -2*x+18*y=13
- -2*x-15*y=-1
- 10*x-2*y=11
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Identical expressions
- x^ two +7x- eighteen = zero
- x squared plus 7x minus 18 equally 0
- x to the power of two plus 7x minus eighteen equally zero
- x2+7x-18=0
- x²+7x-18=0
- x to the power of 2+7x-18=0
- x^2+7x-18=O
-
Similar expressions
- x^2-7x-18=0
- x^2+7x+18=0
x^2+7x-18=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
$$a = 1$$
$$b = 7$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -9$$
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
$$a = 1$$
$$b = 7$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(7)^2 - 4 * (1) * (-18) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -9$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -18$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -18$$
Sum and product of roots
[src]
sum
-9 + 2
$$-9 + 2$$
=
-7
$$-7$$
product
-9*2
$$- 18$$
=
-18
$$-18$$
-18
The graph