Mister Exam
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How to use it?
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Equation x^3=-8
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Equation 4x^2-12x+9=0
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Identical expressions
- (2x+ nine)(4x+ seventeen)= zero
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Similar expressions
- (2x+9)(4x-17)=0
- (2x-9)(4x+17)=0
(2x+9)(4x+17)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(2 x + 9\right) \left(4 x + 17\right) = 0$$
We get the quadratic equation
$$8 x^{2} + 70 x + 153 = 0$$
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
$$a = 8$$
$$b = 70$$
$$c = 153$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{17}{4}$$
$$x_{2} = - \frac{9}{2}$$
$$\left(2 x + 9\right) \left(4 x + 17\right) = 0$$
We get the quadratic equation
$$8 x^{2} + 70 x + 153 = 0$$
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
$$a = 8$$
$$b = 70$$
$$c = 153$$
, then
D = b^2 - 4 * a * c =
(70)^2 - 4 * (8) * (153) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{17}{4}$$
$$x_{2} = - \frac{9}{2}$$
Sum and product of roots
[src]
sum
-9/2 - 17/4
$$- \frac{9}{2} - \frac{17}{4}$$
=
-35/4
$$- \frac{35}{4}$$
product
-9*(-17) -------- 2*4
$$- \frac{-153}{8}$$
=
153/8
$$\frac{153}{8}$$
153/8
Rapid solution
[src]
x1 = -9/2
$$x_{1} = - \frac{9}{2}$$
x2 = -17/4
$$x_{2} = - \frac{17}{4}$$
x2 = -17/4
The graph