Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^4-3x^2-4=0
-
Equation 2^x=8
- Equation x^2-49=0
-
Equation x^3=64
- Express {x} in terms of y where:
- 18*x+19*y=7
- 20*x+9*y=17
- 11*x-11*y=-17
- -2*x-4*y=11
- Derivative of:
-
x^2-49
- Inequation:
- x^2-49
- Factor polynomial:
- x^2-49
-
Identical expressions
- x^ two - forty-nine = zero
- x squared minus 49 equally 0
- x to the power of two minus forty minus nine equally zero
- x2-49=0
- x²-49=0
- x to the power of 2-49=0
- x^2-49=O
-
Similar expressions
- x^2+49=0
x^2-49=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
$$a = 1$$
$$b = 0$$
$$c = -49$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -7$$
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
$$a = 1$$
$$b = 0$$
$$c = -49$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-49) = 196
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -7$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -49$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -49$$
Sum and product of roots
[src]
sum
-7 + 7
$$-7 + 7$$
=
0
$$0$$
product
-7*7
$$- 49$$
=
-49
$$-49$$
-49