Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation z^3=-i
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Equation 3*x^2+x-10=0
-
Equation 2x=5
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Equation sin(x)=(-1)/sqrt(2)
- Express {x} in terms of y where:
- -8*x+14*y=5
- 17*x+7*y=-6
- -11*x-14*y=6
- -18*x-8*y=-5
- Factor polynomial:
- 3*x^2+x-10
-
Identical expressions
- three *x^ two +x- ten = zero
- 3 multiply by x squared plus x minus 10 equally 0
- three multiply by x to the power of two plus x minus ten equally zero
- 3*x2+x-10=0
- 3*x²+x-10=0
- 3*x to the power of 2+x-10=0
- 3x^2+x-10=0
- 3x2+x-10=0
- 3*x^2+x-10=O
-
Similar expressions
- 3*x^2+x+10=0
- 3*x^2-x-10=0
3*x^2+x-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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 3$$
$$b = 1$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{3}$$
$$x_{2} = -2$$
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
$$a = 3$$
$$b = 1$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (3) * (-10) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{3}$$
$$x_{2} = -2$$
Vieta's Theorem
rewrite the equation
$$\left(3 x^{2} + x\right) - 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{3} - \frac{10}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{3}$$
$$x_{1} x_{2} = - \frac{10}{3}$$
$$\left(3 x^{2} + x\right) - 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{3} - \frac{10}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{3}$$
$$x_{1} x_{2} = - \frac{10}{3}$$
Sum and product of roots
[src]
sum
-2 + 5/3
$$-2 + \frac{5}{3}$$
=
-1/3
$$- \frac{1}{3}$$
product
-2*5 ---- 3
$$- \frac{10}{3}$$
=
-10/3
$$- \frac{10}{3}$$
-10/3
The graph