Mister Exam
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How to use it?
- Equation:
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Equation x^2+3x+2=0
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Equation sin(x)=3
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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
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Identical expressions
- x^ two + twenty *x+ ninety-one
- x squared plus 20 multiply by x plus 91
- x to the power of two plus twenty multiply by x plus ninety minus one
- x2+20*x+91
- x²+20*x+91
- x to the power of 2+20*x+91
- x^2+20x+91
- x2+20x+91
-
Similar expressions
- x^2-20*x+91
- x^2+20*x-91
x^2+20*x+91 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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 20$$
$$c = 91$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -7$$
$$x_{2} = -13$$
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
$$a = 1$$
$$b = 20$$
$$c = 91$$
, then
D = b^2 - 4 * a * c =
(20)^2 - 4 * (1) * (91) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -7$$
$$x_{2} = -13$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 20$$
$$q = \frac{c}{a}$$
$$q = 91$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -20$$
$$x_{1} x_{2} = 91$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 20$$
$$q = \frac{c}{a}$$
$$q = 91$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -20$$
$$x_{1} x_{2} = 91$$
Sum and product of roots
[src]
sum
-13 - 7
$$-13 - 7$$
=
-20
$$-20$$
product
-13*(-7)
$$- -91$$
=
91
$$91$$
91