Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2*x^2+5*x-12=0
-
Equation x^2+2x-8=0
-
Equation x^4-10x^2+9=0
-
Equation 7-4(3x-1)=5(1-2x)
- Express {x} in terms of y where:
- 7*x-2*y=18
- 18*x+19*y=7
- 8*x-13*y=-12
- -10*x+13*y=5
- Graphing y =:
- x^2+10*x+16
- Factor polynomial:
- x^2+10*x+16
-
Identical expressions
- x^ two + ten *x+ sixteen = zero
- x squared plus 10 multiply by x plus 16 equally 0
- x to the power of two plus ten multiply by x plus sixteen equally zero
- x2+10*x+16=0
- x²+10*x+16=0
- x to the power of 2+10*x+16=0
- x^2+10x+16=0
- x2+10x+16=0
- x^2+10*x+16=O
-
Similar expressions
- x^2+10*x-16=0
- x^2-10*x+16=0
x^2+10*x+16=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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 10$$
$$c = 16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -8$$
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
$$a = 1$$
$$b = 10$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (16) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = 16$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = 16$$
Sum and product of roots
[src]
sum
-8 - 2
$$-8 - 2$$
=
-10
$$-10$$
product
-8*(-2)
$$- -16$$
=
16
$$16$$
16
The graph