Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x=0
-
Equation -5*x=25
-
Equation 25*x^2=16
- Equation 3*x^2-48=0
- Express {x} in terms of y where:
- 13*x-1*y=-20
- -2*x-18*y=10
- -12*x-11*y=19
- -6*x+11*y=-5
- Sum of series:
-
16
- Derivative of:
-
16
- Integral of d{x}:
-
16
-
Identical expressions
- twenty-five *x^ two = sixteen
- 25 multiply by x squared equally 16
- twenty minus five multiply by x to the power of two equally sixteen
- 25*x2=16
- 25*x²=16
- 25*x to the power of 2=16
- 25x^2=16
- 25x2=16
25*x^2=16 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$25 x^{2} = 16$$
to
$$25 x^{2} - 16 = 0$$
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
$$a = 25$$
$$b = 0$$
$$c = -16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{4}{5}$$
$$x_{2} = - \frac{4}{5}$$
left part with negative sign.
The equation is transformed from
$$25 x^{2} = 16$$
to
$$25 x^{2} - 16 = 0$$
This equation is of the form
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
$$a = 25$$
$$b = 0$$
$$c = -16$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (25) * (-16) = 1600
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{4}{5}$$
$$x_{2} = - \frac{4}{5}$$
Vieta's Theorem
rewrite the equation
$$25 x^{2} = 16$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{16}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{16}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{16}{25}$$
$$25 x^{2} = 16$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{16}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{16}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{16}{25}$$
Sum and product of roots
[src]
sum
-4/5 + 4/5
$$- \frac{4}{5} + \frac{4}{5}$$
=
0
$$0$$
product
-4*4 ---- 5*5
$$- \frac{16}{25}$$
=
-16 ---- 25
$$- \frac{16}{25}$$
-16/25
The graph