Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x/7+x=15/7
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Equation -33-y=-19
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Equation x^2=2x+8
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Equation 6=8-5(7x-1)
- Express {x} in terms of y where:
- -2*x+18*y=13
- -2*x-15*y=-1
- 5*x+4*y=-12
- 10*x-2*y=11
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Identical expressions
- two x^2+x- twenty-one = zero
- 2x squared plus x minus 21 equally 0
- two x squared plus x minus twenty minus one equally zero
- 2x2+x-21=0
- 2x²+x-21=0
- 2x to the power of 2+x-21=0
- 2x^2+x-21=O
-
Similar expressions
- 2x^2+x+21=0
- 2x^2-x-21=0
2x^2+x-21=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
$$a = 2$$
$$b = 1$$
$$c = -21$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
Simplify
$$x_{2} = - \frac{7}{2}$$
Simplify
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
$$a = 2$$
$$b = 1$$
$$c = -21$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (2) * (-21) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
Simplify
$$x_{2} = - \frac{7}{2}$$
Simplify
Vieta's Theorem
rewrite the equation
$$2 x^{2} + x - 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{2} - \frac{21}{2} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{21}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{2}$$
$$x_{1} x_{2} = - \frac{21}{2}$$
$$2 x^{2} + x - 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{2} - \frac{21}{2} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{21}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{2}$$
$$x_{1} x_{2} = - \frac{21}{2}$$
Sum and product of roots
[src]
sum
0 - 7/2 + 3
$$\left(- \frac{7}{2} + 0\right) + 3$$
=
-1/2
$$- \frac{1}{2}$$
product
1*-7/2*3
$$1 \left(- \frac{7}{2}\right) 3$$
=
-21/2
$$- \frac{21}{2}$$
-21/2
The graph