Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x-5=x+7
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Equation z^2-4*z+5=0
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Equation (25+x)-10=40
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Equation x^2+4*x-21=0
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
- Factor polynomial:
- 4*x^2+25
-
Identical expressions
- four *x^ two + twenty-five = zero
- 4 multiply by x squared plus 25 equally 0
- four multiply by x to the power of two plus twenty minus five equally zero
- 4*x2+25=0
- 4*x²+25=0
- 4*x to the power of 2+25=0
- 4x^2+25=0
- 4x2+25=0
- 4*x^2+25=O
-
Similar expressions
- 4*x^2-25=0
4*x^2+25=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
$$a = 4$$
$$b = 0$$
$$c = 25$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{5 i}{2}$$
$$x_{2} = - \frac{5 i}{2}$$
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
$$a = 4$$
$$b = 0$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (4) * (25) = -400
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5 i}{2}$$
$$x_{2} = - \frac{5 i}{2}$$
Vieta's Theorem
rewrite the equation
$$4 x^{2} + 25 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{25}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{25}{4}$$
$$4 x^{2} + 25 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{25}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{25}{4}$$
Rapid solution
[src]
-5*I
x1 = ----
2
$$x_{1} = - \frac{5 i}{2}$$
5*I
x2 = ---
2
$$x_{2} = \frac{5 i}{2}$$
x2 = 5*i/2
Sum and product of roots
[src]
sum
5*I 5*I - --- + --- 2 2
$$- \frac{5 i}{2} + \frac{5 i}{2}$$
=
0
$$0$$
product
-5*I 5*I ----*--- 2 2
$$- \frac{5 i}{2} \frac{5 i}{2}$$
=
25/4
$$\frac{25}{4}$$
25/4