Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x-y=7
-
Equation 1/(x+6)=2
-
Equation (x-4)^2-x^2=0
-
Equation 6/(x+5)=-5
- Express {x} in terms of y where:
- 7*x-1*y=-7
- 10*x-15*y=16
- -14*x-12*y=5
- 13*x-12*y=19
-
Identical expressions
- z^ two + six *z+ ten = zero
- z squared plus 6 multiply by z plus 10 equally 0
- z to the power of two plus six multiply by z plus ten equally zero
- z2+6*z+10=0
- z²+6*z+10=0
- z to the power of 2+6*z+10=0
- z^2+6z+10=0
- z2+6z+10=0
- z^2+6*z+10=O
-
Similar expressions
- z^2+6*z-10=0
- z^2-6*z+10=0
z^2+6*z+10=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:
$$z_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$z_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 6$$
$$c = 10$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$z_{1} = -3 + i$$
$$z_{2} = -3 - i$$
a*z^2 + b*z + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$z_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$z_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 6$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (10) = -4
Because D<0, then the equation
has no real roots,
but complex roots is exists.
z1 = (-b + sqrt(D)) / (2*a)
z2 = (-b - sqrt(D)) / (2*a)
or
$$z_{1} = -3 + i$$
$$z_{2} = -3 - i$$
Vieta's Theorem
it is reduced quadratic equation
$$p z + q + z^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$z_{1} + z_{2} = - p$$
$$z_{1} z_{2} = q$$
$$z_{1} + z_{2} = -6$$
$$z_{1} z_{2} = 10$$
$$p z + q + z^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$z_{1} + z_{2} = - p$$
$$z_{1} z_{2} = q$$
$$z_{1} + z_{2} = -6$$
$$z_{1} z_{2} = 10$$
Sum and product of roots
[src]
sum
-3 - I + -3 + I
$$\left(-3 - i\right) + \left(-3 + i\right)$$
=
-6
$$-6$$
product
(-3 - I)*(-3 + I)
$$\left(-3 - i\right) \left(-3 + i\right)$$
=
10
$$10$$
10
The graph