Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2*x^2-x+5=0
-
Equation e^x=1
-
Equation 5=12-5(4x-1)
-
Equation 10x-20=5x
- Express {x} in terms of y where:
- -12*x-2*y=-15
- -4*x+4*y=-9
- -19*x-2*y=-6
- -2*x+2*y=4
- Graphing y =:
- 2x^2-3x-5
-
Identical expressions
- two x^2-3x- five = zero
- 2x squared minus 3x minus 5 equally 0
- two x squared minus 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
-
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
$$x_{1} = \frac{5}{2}$$
$$x_{2} = -1$$
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
$$x_{1} = \frac{5}{2}$$
$$x_{2} = -1$$
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
$$-1 + \frac{5}{2}$$
=
3/2
$$\frac{3}{2}$$
product
-5 --- 2
$$- \frac{5}{2}$$
=
-5/2
$$- \frac{5}{2}$$
-5/2
The graph