Mister Exam
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How to use it?
- Equation:
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Equation x^2-6*x+12=0
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Equation 2x^2+3*x+1=0
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Equation 6*x^2-18*x+12=0
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Equation (5*x-1)=-2
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Identical expressions
- (y- three)(y+ seven)= zero
- (y minus 3)(y plus 7) equally 0
- (y minus three)(y plus seven) equally zero
- y-3y+7=0
- (y-3)(y+7)=O
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Similar expressions
- (y+3)(y+7)=0
- (y-3)(y-7)=0
- y-(3(y+7)/x)*0=x/2
(y-3)(y+7)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(y - 3\right) \left(y + 7\right) = 0$$
We get the quadratic equation
$$y^{2} + 4 y - 21 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 4$$
$$c = -21$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = 3$$
$$y_{2} = -7$$
$$\left(y - 3\right) \left(y + 7\right) = 0$$
We get the quadratic equation
$$y^{2} + 4 y - 21 = 0$$
This equation is of the form
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 4$$
$$c = -21$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (-21) = 100
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = 3$$
$$y_{2} = -7$$
Sum and product of roots
[src]
sum
-7 + 3
$$-7 + 3$$
=
-4
$$-4$$
product
-7*3
$$- 21$$
=
-21
$$-21$$
-21