Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)/9=(x-3)/2
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Equation x^2-4x+5=0
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Equation x^3=27
- Express {x} in terms of y where:
- -11*x+15*y=7
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Identical expressions
- (-4x- three)*(x- three)= zero
- ( minus 4x minus 3) multiply by (x minus 3) equally 0
- ( minus 4x minus three) multiply by (x minus three) equally zero
- (-4x-3)(x-3)=0
- -4x-3x-3=0
- (-4x-3)*(x-3)=O
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Similar expressions
- (-4*x-3)*(x-3)=0
- (4x-3)*(x-3)=0
- (-4x-3)*(x+3)=0
- (-4x+3)*(x-3)=0
- (-4x-3)(x-3)=0
(-4x-3)*(x-3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 4 x - 3\right) \left(x - 3\right) + 0 = 0$$
We get the quadratic equation
$$- 4 x^{2} + 9 x + 9 = 0$$
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
$$a = -4$$
$$b = 9$$
$$c = 9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{4}$$
Simplify
$$x_{2} = 3$$
Simplify
$$\left(- 4 x - 3\right) \left(x - 3\right) + 0 = 0$$
We get the quadratic equation
$$- 4 x^{2} + 9 x + 9 = 0$$
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
$$a = -4$$
$$b = 9$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (-4) * (9) = 225
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{4}$$
Simplify
$$x_{2} = 3$$
Simplify
Sum and product of roots
[src]
sum
0 - 3/4 + 3
$$\left(- \frac{3}{4} + 0\right) + 3$$
=
9/4
$$\frac{9}{4}$$
product
1*-3/4*3
$$1 \left(- \frac{3}{4}\right) 3$$
=
-9/4
$$- \frac{9}{4}$$
-9/4
The graph