Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
-
Identical expressions
- (15y+ twenty-four)(3y- zero . nine)= zero
- (15y plus 24)(3y minus 0.9) equally 0
- (15y plus twenty minus four)(3y minus zero . nine) equally zero
- 15y+243y-0.9=0
- (15y+24)(3y-0.9)=O
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Similar expressions
- (15y+24)(3y+0.9)=0
- (15y-24)(3y-0.9)=0
(15y+24)(3y-0.9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
(15*y + 24)*(3*y - 9/10) = 0
$$\left(3 y - \frac{9}{10}\right) \left(15 y + 24\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(3 y - \frac{9}{10}\right) \left(15 y + 24\right) = 0$$
We get the quadratic equation
$$45 y^{2} + \frac{117 y}{2} - \frac{108}{5} = 0$$
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
$$a = 45$$
$$b = \frac{117}{2}$$
$$c = - \frac{108}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = \frac{3}{10}$$
$$y_{2} = - \frac{8}{5}$$
$$\left(3 y - \frac{9}{10}\right) \left(15 y + 24\right) = 0$$
We get the quadratic equation
$$45 y^{2} + \frac{117 y}{2} - \frac{108}{5} = 0$$
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
$$a = 45$$
$$b = \frac{117}{2}$$
$$c = - \frac{108}{5}$$
, then
D = b^2 - 4 * a * c =
(117/2)^2 - 4 * (45) * (-108/5) = 29241/4
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = \frac{3}{10}$$
$$y_{2} = - \frac{8}{5}$$
Sum and product of roots
[src]
sum
-8/5 + 3/10
$$- \frac{8}{5} + \frac{3}{10}$$
=
-13 ---- 10
$$- \frac{13}{10}$$
product
-8*3 ---- 5*10
$$- \frac{12}{25}$$
=
-12 ---- 25
$$- \frac{12}{25}$$
-12/25
Rapid solution
[src]
y1 = -8/5
$$y_{1} = - \frac{8}{5}$$
y2 = 3/10
$$y_{2} = \frac{3}{10}$$
y2 = 3/10