Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -6x+2=-x+22
- Equation x^2-x-72=0
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Equation x-5(x+3)=5
- Equation x+y=4
- Express {x} in terms of y where:
- 18*x+19*y=7
- 8*x-13*y=-12
- 1*x+6*y=6
- -2*x-4*y=11
- Graphing y =:
- 2*x^2+3*x-5
- Factor squared:
- 2*x^2+3*x-5
-
Identical expressions
- two *x^ two + three *x- five = zero
- 2 multiply by x squared plus 3 multiply by x minus 5 equally 0
- two multiply by x to the power of two plus three multiply by x minus five equally zero
- 2*x2+3*x-5=0
- 2*x²+3*x-5=0
- 2*x to the power of 2+3*x-5=0
- 2x^2+3x-5=0
- 2x2+3x-5=0
- 2*x^2+3*x-5=O
-
Similar expressions
- 2*x^2-3*x-5=0
- 2*x^2+3*x+5=0
2*x^2+3*x-5=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
$$a = 2$$
$$b = 3$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = - \frac{5}{2}$$
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
$$a = 2$$
$$b = 3$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (2) * (-5) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = - \frac{5}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} + 3 x\right) - 5 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{3 x}{2} - \frac{5}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{3}{2}$$
$$x_{1} x_{2} = - \frac{5}{2}$$
$$\left(2 x^{2} + 3 x\right) - 5 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{3 x}{2} - \frac{5}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{3}{2}$$
$$x_{1} x_{2} = - \frac{5}{2}$$
Sum and product of roots
[src]
sum
1 - 5/2
$$- \frac{5}{2} + 1$$
=
-3/2
$$- \frac{3}{2}$$
product
-5/2
$$- \frac{5}{2}$$
=
-5/2
$$- \frac{5}{2}$$
-5/2
The graph