Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 5*x^2+25*x=0
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Equation 4*x=0
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Equation 5x^2+4x-1=0
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Equation 5(x-4)=3x-10
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Identical expressions
- 5x^ two +4x- one = zero
- 5x squared plus 4x minus 1 equally 0
- 5x to the power of two plus 4x minus one equally zero
- 5x2+4x-1=0
- 5x²+4x-1=0
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- 5x^2+4x-1=O
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Similar expressions
- 5x^2+4x+1=0
- 5x^2-4x-1=0
5x^2+4x-1=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
$$a = 5$$
$$b = 4$$
$$c = -1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{5}$$
$$x_{2} = -1$$
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
$$a = 5$$
$$b = 4$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (5) * (-1) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{5}$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$\left(5 x^{2} + 4 x\right) - 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{4 x}{5} - \frac{1}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{4}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{4}{5}$$
$$x_{1} x_{2} = - \frac{1}{5}$$
$$\left(5 x^{2} + 4 x\right) - 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{4 x}{5} - \frac{1}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{4}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{4}{5}$$
$$x_{1} x_{2} = - \frac{1}{5}$$
Sum and product of roots
[src]
sum
-1 + 1/5
$$-1 + \frac{1}{5}$$
=
-4/5
$$- \frac{4}{5}$$
product
-1 --- 5
$$- \frac{1}{5}$$
=
-1/5
$$- \frac{1}{5}$$
-1/5
The graph