Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2x^2-3x-2=0
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Equation x^2-7*x+10=0
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Equation sin(pi*x)=-1
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Equation x^2-18=7*x
- Express {x} in terms of y where:
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Identical expressions
- (x+ five)(-3x+ nine)= zero
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- (x+5)(-3x+9)=O
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Similar expressions
- (x+5)(3x+9)=0
- (x+5)(-3x-9)=0
- (x-5)(-3x+9)=0
(x+5)(-3x+9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(9 - 3 x\right) \left(x + 5\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} - 6 x + 45 = 0$$
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
$$a = -3$$
$$b = -6$$
$$c = 45$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -5$$
$$x_{2} = 3$$
$$\left(9 - 3 x\right) \left(x + 5\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} - 6 x + 45 = 0$$
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
$$a = -3$$
$$b = -6$$
$$c = 45$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (-3) * (45) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -5$$
$$x_{2} = 3$$
Sum and product of roots
[src]
sum
-5 + 3
$$-5 + 3$$
=
-2
$$-2$$
product
-5*3
$$- 15$$
=
-15
$$-15$$
-15