Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tan(x)=0
-
Equation log(4/(7-x))/log(x^2)=5
-
Equation x-2(3x+2)=16
-
Equation (7x+1)-(9x+3)=5
- Express {x} in terms of y where:
- (x^2+y^2-1)^3-x^2*y^3=0
- -2*x+1*y=-8
- -2*x-1*y=-8
- 4*x+15*y=19
- Canonical form:
- 2x^2-5x-7
- Integral of d{x}:
- 2x^2-5x-7
-
Identical expressions
- two x^2-5x- seven = zero
- 2x squared minus 5x minus 7 equally 0
- two x squared minus 5x minus seven equally zero
- 2x2-5x-7=0
- 2x²-5x-7=0
- 2x to the power of 2-5x-7=0
- 2x^2-5x-7=O
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Similar expressions
- 2x^2+5x-7=0
- 2x^2-5x+7=0
2x^2-5x-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
$$a = 2$$
$$b = -5$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{7}{2}$$
Simplify
$$x_{2} = -1$$
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
$$a = 2$$
$$b = -5$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (2) * (-7) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{7}{2}$$
Simplify
$$x_{2} = -1$$
Simplify
Vieta's Theorem
rewrite the equation
$$2 x^{2} - 5 x - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} - \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = - \frac{7}{2}$$
$$2 x^{2} - 5 x - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} - \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = - \frac{7}{2}$$
Sum and product of roots
[src]
sum
0 - 1 + 7/2
$$\left(-1 + 0\right) + \frac{7}{2}$$
=
5/2
$$\frac{5}{2}$$
product
1*-1*7/2
$$1 \left(-1\right) \frac{7}{2}$$
=
-7/2
$$- \frac{7}{2}$$
-7/2