Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)-x=0
-
Equation 15-4(7-x)=11
-
Equation x+(8-3x)=12
-
Equation 3*x-4/6=7/8
- Express {x} in terms of y where:
- 2*x+11*y=0
- 14*x-17*y=-4
- 18*x-10*y=-9
- -16*x-14*y=-18
- Factor squared:
- x^2-7*x+5
- Graphing y =:
- x^2-7*x+5
-
Identical expressions
- x^ two - seven *x+ five = zero
- x squared minus 7 multiply by x plus 5 equally 0
- x to the power of two minus seven multiply by x plus five equally zero
- x2-7*x+5=0
- x²-7*x+5=0
- x to the power of 2-7*x+5=0
- x^2-7x+5=0
- x2-7x+5=0
- x^2-7*x+5=O
-
Similar expressions
- x^2+7*x+5=0
- x^2-7*x-5=0
x^2-7*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
$$a = 1$$
$$b = -7$$
$$c = 5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{29}}{2} + \frac{7}{2}$$
$$x_{2} = \frac{7}{2} - \frac{\sqrt{29}}{2}$$
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
$$a = 1$$
$$b = -7$$
$$c = 5$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (1) * (5) = 29
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{29}}{2} + \frac{7}{2}$$
$$x_{2} = \frac{7}{2} - \frac{\sqrt{29}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 5$$
Rapid solution
[src]
____
7 \/ 29
x1 = - - ------
2 2
$$x_{1} = \frac{7}{2} - \frac{\sqrt{29}}{2}$$
____
7 \/ 29
x2 = - + ------
2 2
$$x_{2} = \frac{\sqrt{29}}{2} + \frac{7}{2}$$
x2 = sqrt(29)/2 + 7/2
Sum and product of roots
[src]
sum
____ ____ 7 \/ 29 7 \/ 29 - - ------ + - + ------ 2 2 2 2
$$\left(\frac{7}{2} - \frac{\sqrt{29}}{2}\right) + \left(\frac{\sqrt{29}}{2} + \frac{7}{2}\right)$$
=
7
$$7$$
product
/ ____\ / ____\ |7 \/ 29 | |7 \/ 29 | |- - ------|*|- + ------| \2 2 / \2 2 /
$$\left(\frac{7}{2} - \frac{\sqrt{29}}{2}\right) \left(\frac{\sqrt{29}}{2} + \frac{7}{2}\right)$$
=
5
$$5$$
5
The graph