Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a*x=b
-
Equation x^2-x+8=0
-
Equation 2^x=7
-
Equation 3x^2-2x=0
- Express {x} in terms of y where:
- 2*x+19*y=-7
- -4*x+7*y=-16
- -16*x+3*y=17
- 12*x-20*y=9
- Factor polynomial:
- x^2+7*x+5
-
Identical expressions
- x^ two + seven *x+ five = zero
- x squared plus 7 multiply by x plus 5 equally 0
- x to the power of two plus 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
$$x_{1} = - \frac{7}{2} + \frac{\sqrt{29}}{2}$$
$$x_{2} = - \frac{7}{2} - \frac{\sqrt{29}}{2}$$
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
$$x_{1} = - \frac{7}{2} + \frac{\sqrt{29}}{2}$$
$$x_{2} = - \frac{7}{2} - \frac{\sqrt{29}}{2}$$
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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = 5$$
Sum and product of roots
[src]
sum
____ ____ 7 \/ 29 7 \/ 29 - - - ------ + - - + ------ 2 2 2 2
$$\left(- \frac{7}{2} - \frac{\sqrt{29}}{2}\right) + \left(- \frac{7}{2} + \frac{\sqrt{29}}{2}\right)$$
=
-7
$$-7$$
product
/ ____\ / ____\ | 7 \/ 29 | | 7 \/ 29 | |- - - ------|*|- - + ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{7}{2} - \frac{\sqrt{29}}{2}\right) \left(- \frac{7}{2} + \frac{\sqrt{29}}{2}\right)$$
=
5
$$5$$
5
Rapid solution
[src]
____
7 \/ 29
x1 = - - - ------
2 2
$$x_{1} = - \frac{7}{2} - \frac{\sqrt{29}}{2}$$
____
7 \/ 29
x2 = - - + ------
2 2
$$x_{2} = - \frac{7}{2} + \frac{\sqrt{29}}{2}$$
x2 = -7/2 + sqrt(29)/2