Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4=(4*x-21)^2
-
Equation (7x+1)-(9x+3)=5
-
Equation (x+2)^2+(x-3)^2=2x^2
-
Equation sin(x)=3/2
- Express {x} in terms of y where:
- -14*x-3*y=-5
- -19*x-14*y=-8
- 9*x+8*y=6
- 4*x+16*y=6
- Derivative of:
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x^2-7x
- Graphing y =:
- x^2-7x
- Integral of d{x}:
- x^2-7x
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Identical expressions
- x^ two -7x= zero
- x squared minus 7x equally 0
- x to the power of two minus 7x equally zero
- x2-7x=0
- x²-7x=0
- x to the power of 2-7x=0
- x^2-7x=O
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Similar expressions
- -2*x+4*x+5=2*x^2-7*x+2*x-3
- x^2+7x=0
x^2-7x=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
$$a = 1$$
$$b = -7$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = 0$$
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
$$a = 1$$
$$b = -7$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (1) * (0) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = 0$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 0$$
The graph