Mister Exam
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How to use it?
- Equation:
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Equation x^2+9x+20=0
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Equation log(27)*x=1/3
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Equation x^2+4x-32=0
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Equation 4x^2+20x=0
- Express {x} in terms of y where:
- 15*x+15*y=16
- -4*x+18*y=-14
- 8*x+7*y=-13
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Identical expressions
- x^ two +4x- thirty-two = zero
- x squared plus 4x minus 32 equally 0
- x to the power of two plus 4x minus thirty minus two equally zero
- x2+4x-32=0
- x²+4x-32=0
- x to the power of 2+4x-32=0
- x^2+4x-32=O
-
Similar expressions
- x^2-4x-32=0
- x^2+4x+32=0
x^2+4x-32=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
$$a = 1$$
$$b = 4$$
$$c = -32$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -8$$
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
$$a = 1$$
$$b = 4$$
$$c = -32$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (-32) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -8$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -32$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -32$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -32$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -32$$
Sum and product of roots
[src]
sum
0 - 8 + 4
$$\left(-8 + 0\right) + 4$$
=
-4
$$-4$$
product
1*-8*4
$$1 \left(-8\right) 4$$
=
-32
$$-32$$
-32
The graph