Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=-3
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Equation 4(x-6)=7(x+9)
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Equation 7x+5=9x-11
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Equation -5*x^2+x=0
- Express {x} in terms of y where:
- -2*x+5*y=0
- 10*x-13*y=16
- -17*x-2*y=17
- -11*x+10*y=18
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Identical expressions
- (5x- one)*(2x+ four)= zero
- (5x minus 1) multiply by (2x plus 4) equally 0
- (5x minus one) multiply by (2x plus four) equally zero
- (5x-1)(2x+4)=0
- 5x-12x+4=0
- (5x-1)*(2x+4)=O
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Similar expressions
- (5x+1)*(2x+4)=0
- (5x-1)*(2x-4)=0
(5x-1)*(2x+4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(2 x + 4\right) \left(5 x - 1\right) = 0$$
We get the quadratic equation
$$10 x^{2} + 18 x - 4 = 0$$
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
$$a = 10$$
$$b = 18$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{5}$$
$$x_{2} = -2$$
$$\left(2 x + 4\right) \left(5 x - 1\right) = 0$$
We get the quadratic equation
$$10 x^{2} + 18 x - 4 = 0$$
This equation is of the form
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
$$a = 10$$
$$b = 18$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(18)^2 - 4 * (10) * (-4) = 484
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{5}$$
$$x_{2} = -2$$
Sum and product of roots
[src]
sum
-2 + 1/5
$$-2 + \frac{1}{5}$$
=
-9/5
$$- \frac{9}{5}$$
product
-2 --- 5
$$- \frac{2}{5}$$
=
-2/5
$$- \frac{2}{5}$$
-2/5