Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)-cos(x)=1
-
Equation 2-3(7+2x)=11
-
Equation 18-x^2=14
-
Equation 2x^2+8=0
- Express {x} in terms of y where:
- 4*x+15*y=19
- -14*x-16*y=14
- 18*x+14*y=-11
- -6*x-2*y=-10
-
Identical expressions
- y^ two +2y- thirty-five = zero
- y squared plus 2y minus 35 equally 0
- y to the power of two plus 2y minus thirty minus five equally zero
- y2+2y-35=0
- y²+2y-35=0
- y to the power of 2+2y-35=0
- y^2+2y-35=O
-
Similar expressions
- y^2+2y+35=0
- y^2-2y-35=0
y^2+2y-35=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = 2$$
$$c = -35$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = 5$$
$$y_{2} = -7$$
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
$$a = 1$$
$$b = 2$$
$$c = -35$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (-35) = 144
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = 5$$
$$y_{2} = -7$$
Vieta's Theorem
it is reduced quadratic equation
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -2$$
$$y_{1} y_{2} = -35$$
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -2$$
$$y_{1} y_{2} = -35$$
Sum and product of roots
[src]
sum
-7 + 5
$$-7 + 5$$
=
-2
$$-2$$
product
-7*5
$$- 35$$
=
-35
$$-35$$
-35