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