Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5(x-4)=3x-10
-
Equation |x|=-1
-
Equation tan(x)=7
-
Equation 6-3*(x+1)=7-2*x
- Express {x} in terms of y where:
- 13*x-1*y=-4
- -17*x+6*y=14
- -15*x-5*y=12
- -1*x+11*y=-9
-
Identical expressions
- 3x^ two +13x- ten = zero
- 3x squared plus 13x minus 10 equally 0
- 3x to the power of two plus 13x minus ten equally zero
- 3x2+13x-10=0
- 3x²+13x-10=0
- 3x to the power of 2+13x-10=0
- 3x^2+13x-10=O
-
Similar expressions
- 3x^2+13x+10=0
- 3x^2-13x-10=0
3x^2+13x-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
$$a = 3$$
$$b = 13$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{3}$$
$$x_{2} = -5$$
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
$$a = 3$$
$$b = 13$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(13)^2 - 4 * (3) * (-10) = 289
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{3}$$
$$x_{2} = -5$$
Vieta's Theorem
rewrite the equation
$$\left(3 x^{2} + 13 x\right) - 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{13 x}{3} - \frac{10}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{13}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{13}{3}$$
$$x_{1} x_{2} = - \frac{10}{3}$$
$$\left(3 x^{2} + 13 x\right) - 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{13 x}{3} - \frac{10}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{13}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{13}{3}$$
$$x_{1} x_{2} = - \frac{10}{3}$$
Sum and product of roots
[src]
sum
-5 + 2/3
$$-5 + \frac{2}{3}$$
=
-13/3
$$- \frac{13}{3}$$
product
-5*2 ---- 3
$$- \frac{10}{3}$$
=
-10/3
$$- \frac{10}{3}$$
-10/3
The graph