Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation 3*x^2-48=0
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Equation 4(x-1)=2(2x-8)+12
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Equation x^2-18=7*x
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Equation (x-4)/4=(x+3)/7
- Express {x} in terms of y where:
- 4*x+13*y=8
- 14*x+17*y=19
- 3*x-11*y=20
- -18*x-13*y=2
- Graphing y =:
- 2x^2+3x-5
-
Identical expressions
- two x^2+3x- five = zero
- 2x squared plus 3x minus 5 equally 0
- two x squared plus 3x minus five equally zero
- 2x2+3x-5=0
- 2x²+3x-5=0
- 2x to the power of 2+3x-5=0
- 2x^2+3x-5=O
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Similar expressions
- 2x^2-3x-5=0
- 2x^2+3x+5=0
2x^2+3x-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