Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x^2-8=0
-
Equation x^2-3x+5=0
-
Equation x^2+10*x+24=0
-
Equation (x-8)^2=(x-2)^2
- Express {x} in terms of y where:
- -14*x-3*y=-14
- 4*x-8*y=10
- -1*x-14*y=5
- 18*x-7*y=3
- Factor polynomial:
- 6*x^2-x-1
- Factor squared:
- 6*x^2-x-1
-
Identical expressions
- six *x^ two -x- one = zero
- 6 multiply by x squared minus x minus 1 equally 0
- six multiply by x to the power of two minus x minus one equally zero
- 6*x2-x-1=0
- 6*x²-x-1=0
- 6*x to the power of 2-x-1=0
- 6x^2-x-1=0
- 6x2-x-1=0
- 6*x^2-x-1=O
-
Similar expressions
- 6*x^2+x-1=0
- 6*x^2-x+1=0
6*x^2-x-1=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
$$a = 6$$
$$b = -1$$
$$c = -1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = - \frac{1}{3}$$
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
$$a = 6$$
$$b = -1$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (6) * (-1) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = - \frac{1}{3}$$
Vieta's Theorem
rewrite the equation
$$\left(6 x^{2} - x\right) - 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{6} - \frac{1}{6} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{6}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{6}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{6}$$
$$x_{1} x_{2} = - \frac{1}{6}$$
$$\left(6 x^{2} - x\right) - 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{6} - \frac{1}{6} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{6}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{6}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{6}$$
$$x_{1} x_{2} = - \frac{1}{6}$$
Sum and product of roots
[src]
sum
-1/3 + 1/2
$$- \frac{1}{3} + \frac{1}{2}$$
=
1/6
$$\frac{1}{6}$$
product
-1 --- 3*2
$$- \frac{1}{6}$$
=
-1/6
$$- \frac{1}{6}$$
-1/6