Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x^2-1)/(x+2)=4x
-
Equation cos(x/2)=(1/2)
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Equation x+2x²-4=8+3x²-7x
-
Equation 119*z^2+6=(7*z+1)*(17*z+7)
- Express {x} in terms of y where:
- 15*x-3*y=19
- -10*x+9*y=-6
- 16*x+7*y=8
- -4*x-18*y=-14
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Identical expressions
- x²+17x- thirty-eight = zero
- x² plus 17x minus 38 equally 0
- x² plus 17x minus thirty minus eight equally zero
- x²+17x-38=O
-
Similar expressions
- x²-17x-38=0
- x²+17x+38=0
x²+17x-38=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
$$a = 1$$
$$b = 17$$
$$c = -38$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -19$$
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
$$a = 1$$
$$b = 17$$
$$c = -38$$
, then
D = b^2 - 4 * a * c =
(17)^2 - 4 * (1) * (-38) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -19$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 17$$
$$q = \frac{c}{a}$$
$$q = -38$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -17$$
$$x_{1} x_{2} = -38$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 17$$
$$q = \frac{c}{a}$$
$$q = -38$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -17$$
$$x_{1} x_{2} = -38$$
Sum and product of roots
[src]
sum
-19 + 2
$$-19 + 2$$
=
-17
$$-17$$
product
-19*2
$$- 38$$
=
-38
$$-38$$
-38