Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-2=0
-
Equation x+(x*3)=168
- Equation x-1=1+(1/2)*y
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Equation -4+x/5=x+4/2
- Express {x} in terms of y where:
- 15*x+2*y=8
- 1*x+4*y=-11
- 5*x-18*y=-17
- -9*x+6*y=18
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Identical expressions
- (5x+ three)(x- two)= zero
- (5x plus 3)(x minus 2) equally 0
- (5x plus three)(x minus two) equally zero
- 5x+3x-2=0
- (5x+3)(x-2)=O
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Similar expressions
- (5x-3)(x-2)=0
- (5x+3)(x+2)=0
(5x+3)(x-2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 2\right) \left(5 x + 3\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 7 x - 6 = 0$$
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
$$a = 5$$
$$b = -7$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = - \frac{3}{5}$$
$$\left(x - 2\right) \left(5 x + 3\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 7 x - 6 = 0$$
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
$$a = 5$$
$$b = -7$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (5) * (-6) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = - \frac{3}{5}$$
Sum and product of roots
[src]
sum
2 - 3/5
$$- \frac{3}{5} + 2$$
=
7/5
$$\frac{7}{5}$$
product
2*(-3) ------ 5
$$\frac{\left(-3\right) 2}{5}$$
=
-6/5
$$- \frac{6}{5}$$
-6/5