Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 15-16x+4x^2=0
-
Equation ctg(x)=-5
- Equation 3a^2-21=0
- Equation 4+(2x-(4x-1))+x=-5-x
- Express {x} in terms of y where:
- 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|
- 10*x-1*y=10
-
Identical expressions
- 3a^ two - twenty-one = zero
- 3a squared minus 21 equally 0
- 3a to the power of two minus twenty minus one equally zero
- 3a2-21=0
- 3a²-21=0
- 3a to the power of 2-21=0
- 3a^2-21=O
-
Similar expressions
- 3a^2+21=0
3a^2-21=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:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 3$$
$$b = 0$$
$$c = -21$$
, then
Because D > 0, then the equation has two roots.
or
$$a_{1} = \sqrt{7}$$
$$a_{2} = - \sqrt{7}$$
a*a^2 + b*a + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 3$$
$$b = 0$$
$$c = -21$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-21) = 252
Because D > 0, then the equation has two roots.
a1 = (-b + sqrt(D)) / (2*a)
a2 = (-b - sqrt(D)) / (2*a)
or
$$a_{1} = \sqrt{7}$$
$$a_{2} = - \sqrt{7}$$
Vieta's Theorem
rewrite the equation
$$3 a^{2} - 21 = 0$$
of
$$a^{3} + a b + c = 0$$
as reduced quadratic equation
$$a^{2} + b + \frac{c}{a} = 0$$
$$a^{2} - 7 = 0$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = 0$$
$$a_{1} a_{2} = -7$$
$$3 a^{2} - 21 = 0$$
of
$$a^{3} + a b + c = 0$$
as reduced quadratic equation
$$a^{2} + b + \frac{c}{a} = 0$$
$$a^{2} - 7 = 0$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = 0$$
$$a_{1} a_{2} = -7$$
Rapid solution
[src]
___ a1 = -\/ 7
$$a_{1} = - \sqrt{7}$$
___ a2 = \/ 7
$$a_{2} = \sqrt{7}$$
a2 = sqrt(7)
Sum and product of roots
[src]
sum
___ ___ - \/ 7 + \/ 7
$$- \sqrt{7} + \sqrt{7}$$
=
0
$$0$$
product
___ ___ -\/ 7 *\/ 7
$$- \sqrt{7} \sqrt{7}$$
=
-7
$$-7$$
-7