Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x-3=7x-3(2x-5)
-
Equation 12x+5(6-3x)=10-3x
- Equation x^5-32=0
-
Equation k^2+k-6=0
- Express {x} in terms of y where:
- -10*x-16*y=-6
- 16*x+7*y=8
- -11*x+4*y=-8
- 17*x-11*y=2
-
Identical expressions
- k^ two +k- six = zero
- k squared plus k minus 6 equally 0
- k to the power of two plus k minus six equally zero
- k2+k-6=0
- k²+k-6=0
- k to the power of 2+k-6=0
- k^2+k-6=O
-
Similar expressions
- k^2-k-6=0
- k^2+k+6=0
k^2+k-6=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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$k_{1} = 2$$
$$k_{2} = -3$$
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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-6) = 25
Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 2$$
$$k_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = -1$$
$$k_{1} k_{2} = -6$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = -1$$
$$k_{1} k_{2} = -6$$
Sum and product of roots
[src]
sum
-3 + 2
$$-3 + 2$$
=
-1
$$-1$$
product
-3*2
$$- 6$$
=
-6
$$-6$$
-6
The graph