Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+2x+1=0
-
Equation 25-x^2=0
-
Equation sinx=1
-
Equation cosx=1/2
- Express {x} in terms of y where:
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- sqrt(x)+sqrt(y)=69,49
- (x^2+y^2)×(x+y-3)=2xy
- sqrt(1-x)^2+(4-y)^2=0
- Integral of d{x}:
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25-x^2
- Graphing y =:
- 25-x^2
- Limit of the function:
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25-x^2
-
Identical expressions
- twenty-five -x^ two = zero
- 25 minus x squared equally 0
- twenty minus five minus x to the power of two equally zero
- 25-x2=0
- 25-x²=0
- 25-x to the power of 2=0
- 25-x^2=O
-
Similar expressions
- 25+x^2=0
25-x^2=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
$$a = -1$$
$$b = 0$$
$$c = 25$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -5$$
$$x_{2} = 5$$
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
$$a = -1$$
$$b = 0$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (25) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -5$$
$$x_{2} = 5$$
Vieta's Theorem
rewrite the equation
$$25 - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 25 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -25$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -25$$
$$25 - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 25 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -25$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -25$$
Sum and product of roots
[src]
sum
-5 + 5
$$-5 + 5$$
=
0
$$0$$
product
-5*5
$$- 25$$
=
-25
$$-25$$
-25
The graph