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- Equation:
-
Equation 3x²-27=0
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Identical expressions
- 3x²- twenty-seven = zero
- 3x² minus 27 equally 0
- 3x² minus twenty minus seven equally zero
- 3x²-27=O
-
Similar expressions
- (1/3)x²-27=0
- 3x²+27=0
3x²-27=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
$$a = 3$$
$$b = 0$$
$$c = -27$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
Simplify
$$x_{2} = -3$$
Simplify
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
$$a = 3$$
$$b = 0$$
$$c = -27$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-27) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
Simplify
$$x_{2} = -3$$
Simplify
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 27 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 9 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -9$$
$$3 x^{2} - 27 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 9 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -9$$
Sum and product of roots
[src]
sum
0 - 3 + 3
$$\left(-3 + 0\right) + 3$$
=
0
$$0$$
product
1*-3*3
$$1 \left(-3\right) 3$$
=
-9
$$-9$$
-9
The graph