Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-4x+6=0
-
Equation cos(4*x)=0
-
Equation x^2-21=4x
-
Equation 5x-9=3x+1
- Express {x} in terms of y where:
- -12*x+17*y=-11
- -8*x-16*y=18
- -10*x-19*y=3
- -4*x+18*y=10
- Derivative of:
- 3x^2-7
-
Identical expressions
- 3x^ two - seven = zero
- 3x squared minus 7 equally 0
- 3x to the power of two minus seven equally zero
- 3x2-7=0
- 3x²-7=0
- 3x to the power of 2-7=0
- 3x^2-7=O
-
Similar expressions
- 3x^2+7=0
3x^2-7=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
$$a = 3$$
$$b = 0$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{21}}{3}$$
$$x_{2} = - \frac{\sqrt{21}}{3}$$
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
$$a = 3$$
$$b = 0$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-7) = 84
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{21}}{3}$$
$$x_{2} = - \frac{\sqrt{21}}{3}$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{7}{3}$$
$$3 x^{2} - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{7}{3}$$
Rapid solution
[src]
____
-\/ 21
x1 = --------
3
$$x_{1} = - \frac{\sqrt{21}}{3}$$
____
\/ 21
x2 = ------
3
$$x_{2} = \frac{\sqrt{21}}{3}$$
x2 = sqrt(21)/3
Sum and product of roots
[src]
sum
____ ____
\/ 21 \/ 21
- ------ + ------
3 3
$$- \frac{\sqrt{21}}{3} + \frac{\sqrt{21}}{3}$$
=
0
$$0$$
product
____ ____ -\/ 21 \/ 21 --------*------ 3 3
$$- \frac{\sqrt{21}}{3} \frac{\sqrt{21}}{3}$$
=
-7/3
$$- \frac{7}{3}$$
-7/3