Mister Exam
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How to use it?
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Equation 12x+5(6-3x)=10-3x
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Equation x^2+x-42=0
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Equation k^2+16=0
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Identical expressions
- k^ two + sixteen = zero
- k squared plus 16 equally 0
- k to the power of two plus sixteen equally zero
- k2+16=0
- k²+16=0
- k to the power of 2+16=0
- k^2+16=O
-
Similar expressions
- k^2-16=0
k^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:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
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 no real roots,
but complex roots is exists.
or
$$k_{1} = 4 i$$
$$k_{2} = - 4 i$$
a*k^2 + b*k + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
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 no real roots,
but complex roots is exists.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 4 i$$
$$k_{2} = - 4 i$$
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 16$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 16$$
Sum and product of roots
[src]
sum
-4*I + 4*I
$$- 4 i + 4 i$$
=
0
$$0$$
product
-4*I*4*I
$$- 4 i 4 i$$
=
16
$$16$$
16
The graph