Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=-100
-
Equation 9+10(3x-10)=2
-
Equation -7*x=4
-
Equation 10x-2(4x-5)=2x+10
- Express {x} in terms of y where:
- 4*x-4*y=-19
- -16*x+18*y=9
- 4*x-1*y=12
- 7*x-19*y=-8
-
Identical expressions
- 3x^ two +8x- twenty-eight = zero
- 3x squared plus 8x minus 28 equally 0
- 3x to the power of two plus 8x minus twenty minus eight equally zero
- 3x2+8x-28=0
- 3x²+8x-28=0
- 3x to the power of 2+8x-28=0
- 3x^2+8x-28=O
-
Similar expressions
- 3x^2-8x-28=0
- 3x^2+8x+28=0
3x^2+8x-28=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
$$a = 3$$
$$b = 8$$
$$c = -28$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = - \frac{14}{3}$$
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
$$a = 3$$
$$b = 8$$
$$c = -28$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (3) * (-28) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = - \frac{14}{3}$$
Vieta's Theorem
rewrite the equation
$$\left(3 x^{2} + 8 x\right) - 28 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{8 x}{3} - \frac{28}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{8}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{28}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{8}{3}$$
$$x_{1} x_{2} = - \frac{28}{3}$$
$$\left(3 x^{2} + 8 x\right) - 28 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{8 x}{3} - \frac{28}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{8}{3}$$
$$q = \frac{c}{a}$$
$$q = - \frac{28}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{8}{3}$$
$$x_{1} x_{2} = - \frac{28}{3}$$
Sum and product of roots
[src]
sum
2 - 14/3
$$- \frac{14}{3} + 2$$
=
-8/3
$$- \frac{8}{3}$$
product
2*(-14) ------- 3
$$\frac{\left(-14\right) 2}{3}$$
=
-28/3
$$- \frac{28}{3}$$
-28/3