Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation a^2*x^2-21*a^2+a*x+1=0
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Equation -(-y+4)+2*y+1=0
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Equation 3^x=8
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Equation 5*cos(x)=6
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 12*x-14*y=5
- -19*x-2*y=2
- -20*x-4*y=-14
- Graphing y =:
- x^2+3*x-7
- Factor polynomial:
- x^2+3*x-7
-
Identical expressions
- x^ two + three *x- seven = zero
- x squared plus 3 multiply by x minus 7 equally 0
- x to the power of two plus three multiply by x minus seven equally zero
- x2+3*x-7=0
- x²+3*x-7=0
- x to the power of 2+3*x-7=0
- x^2+3x-7=0
- x2+3x-7=0
- x^2+3*x-7=O
-
Similar expressions
- x^2-3*x-7=0
- x^2+3*x+7=0
x^2+3*x-7=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
$$a = 1$$
$$b = 3$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{37}}{2}$$
$$x_{2} = - \frac{\sqrt{37}}{2} - \frac{3}{2}$$
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
$$a = 1$$
$$b = 3$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (1) * (-7) = 37
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{37}}{2}$$
$$x_{2} = - \frac{\sqrt{37}}{2} - \frac{3}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -7$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -7$$
Sum and product of roots
[src]
sum
____ ____ 3 \/ 37 3 \/ 37 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{37}}{2} - \frac{3}{2}\right) + \left(- \frac{3}{2} + \frac{\sqrt{37}}{2}\right)$$
=
-3
$$-3$$
product
/ ____\ / ____\ | 3 \/ 37 | | 3 \/ 37 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{3}{2} + \frac{\sqrt{37}}{2}\right) \left(- \frac{\sqrt{37}}{2} - \frac{3}{2}\right)$$
=
-7
$$-7$$
-7
Rapid solution
[src]
____
3 \/ 37
x1 = - - + ------
2 2
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{37}}{2}$$
____
3 \/ 37
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{37}}{2} - \frac{3}{2}$$
x2 = -sqrt(37)/2 - 3/2
The graph