Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5*x^2+25*x=0
-
Equation 4*x=0
-
Equation 5(x-4)=3x-10
-
Equation x^4=(4*x-5)^2
- Express {x} in terms of y where:
- -1*x-20*y=1
- -3*x-1*y=-9
- -19*x+10*y=-3
- 16*x+11*y=4
-
Identical expressions
- twenty-five *x^ two - four = zero
- 25 multiply by x squared minus 4 equally 0
- twenty minus five multiply by x to the power of two minus four equally zero
- 25*x2-4=0
- 25*x²-4=0
- 25*x to the power of 2-4=0
- 25x^2-4=0
- 25x2-4=0
- 25*x^2-4=O
-
Similar expressions
- 25*x^2+4=0
25*x^2-4=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
$$a = 25$$
$$b = 0$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = - \frac{2}{5}$$
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
$$a = 25$$
$$b = 0$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (25) * (-4) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = - \frac{2}{5}$$
Vieta's Theorem
rewrite the equation
$$25 x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{4}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{4}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{4}{25}$$
$$25 x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{4}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{4}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{4}{25}$$
Sum and product of roots
[src]
sum
-2/5 + 2/5
$$- \frac{2}{5} + \frac{2}{5}$$
=
0
$$0$$
product
-2*2 ---- 5*5
$$- \frac{4}{25}$$
=
-4/25
$$- \frac{4}{25}$$
-4/25
The graph