Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (2x-4)(x-11)+28=0
- Equation 3x^2-28x+9=0
- Equation 5-8cos^2x=sin2x
- Equation (4+x*9)-36=40
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
-
Identical expressions
- 3x^ two -28x+ nine = zero
- 3x squared minus 28x plus 9 equally 0
- 3x to the power of two minus 28x plus nine equally zero
- 3x2-28x+9=0
- 3x²-28x+9=0
- 3x to the power of 2-28x+9=0
- 3x^2-28x+9=O
-
Similar expressions
- 3x^2-28x-9=0
- 3x^2+28x+9=0
3x^2-28x+9=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
$$a = 3$$
$$b = -28$$
$$c = 9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = \frac{1}{3}$$
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
$$a = 3$$
$$b = -28$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-28)^2 - 4 * (3) * (9) = 676
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = \frac{1}{3}$$
Vieta's Theorem
rewrite the equation
$$\left(3 x^{2} - 28 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{28 x}{3} + 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{28}{3}$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{28}{3}$$
$$x_{1} x_{2} = 3$$
$$\left(3 x^{2} - 28 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{28 x}{3} + 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{28}{3}$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{28}{3}$$
$$x_{1} x_{2} = 3$$
Sum and product of roots
[src]
sum
9 + 1/3
$$\frac{1}{3} + 9$$
=
28/3
$$\frac{28}{3}$$
product
9 - 3
$$\frac{9}{3}$$
=
3
$$3$$
3