Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 10*(x-9)=7
-
Equation 3-3*6+2=x
-
Equation 9/(x-2)=9/2
-
Equation sin(x-pi/3)=0
- Express {x} in terms of y where:
- -9*x-4*y=-20
- -9*x-15*y=-4
- 12*x-14*y=20
- -11*x+10*y=-9
-
Identical expressions
- x^ two + ten *x- ninety-six = zero
- x squared plus 10 multiply by x minus 96 equally 0
- x to the power of two plus ten multiply by x minus ninety minus six equally zero
- x2+10*x-96=0
- x²+10*x-96=0
- x to the power of 2+10*x-96=0
- x^2+10x-96=0
- x2+10x-96=0
- x^2+10*x-96=O
-
Similar expressions
- x^2-10*x-96=0
- x^2+10*x+96=0
x^2+10*x-96=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
$$a = 1$$
$$b = 10$$
$$c = -96$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = -16$$
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
$$a = 1$$
$$b = 10$$
$$c = -96$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (-96) = 484
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = -16$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = -96$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = -96$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = -96$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = -96$$
Sum and product of roots
[src]
sum
-16 + 6
$$-16 + 6$$
=
-10
$$-10$$
product
-16*6
$$- 96$$
=
-96
$$-96$$
-96