Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4+2*x^2-8=0
-
Equation x^4+4=0
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Equation 3(x+3)=2x+5
- Equation x+y=3
- Express {x} in terms of y where:
- 2*x+13*y=19
- -17*x+18*y=10
- 7*x-1*y=-7
- 10*x-18*y=3
-
Identical expressions
- (-4x- three)(x- three)= zero
- ( minus 4x minus 3)(x minus 3) equally 0
- ( minus 4x minus three)(x minus three) equally zero
- -4x-3x-3=0
- (-4x-3)(x-3)=O
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Similar expressions
- (4x-3)(x-3)=0
- (-4x+3)(x-3)=0
- (-4x-3)(x+3)=0
- (-4*x-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
$$\left(- 4 x - 3\right) \left(x - 3\right) = 0$$
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
$$x_{1} = - \frac{3}{4}$$
$$x_{2} = 3$$
$$\left(- 4 x - 3\right) \left(x - 3\right) = 0$$
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
$$x_{1} = - \frac{3}{4}$$
$$x_{2} = 3$$
Sum and product of roots
[src]
sum
3 - 3/4
$$- \frac{3}{4} + 3$$
=
9/4
$$\frac{9}{4}$$
product
3*(-3) ------ 4
$$\frac{\left(-3\right) 3}{4}$$
=
-9/4
$$- \frac{9}{4}$$
-9/4
The graph