Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5*x^2+25*x=0
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Equation -2x+16=5x+30
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Equation y^2-16=0
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Equation -4*(-z+7)=z+17
- Express {x} in terms of y where:
- -4*x-12*y=13
- 16*x+14*y=-14
- 11*x-15*y=3
- 3*x-14*y=-2
- Factor polynomial:
- y^2-16
-
Identical expressions
- y^ two - sixteen = zero
- y squared minus 16 equally 0
- y to the power of two minus sixteen equally zero
- y2-16=0
- y²-16=0
- y to the power of 2-16=0
- y^2-16=O
-
Similar expressions
- y^2+16=0
y^2-16=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:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = -16$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = 4$$
$$y_{2} = -4$$
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = -16$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-16) = 64
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = 4$$
$$y_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 0$$
$$y_{1} y_{2} = -16$$
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 0$$
$$y_{1} y_{2} = -16$$
Sum and product of roots
[src]
sum
-4 + 4
$$-4 + 4$$
=
0
$$0$$
product
-4*4
$$- 16$$
=
-16
$$-16$$
-16
The graph