Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation ax=b
- Equation a*x=b
-
Equation x^2-x+8=0
-
Equation 2^x=7
- Express {x} in terms of y where:
- -4*x+7*y=-16
- -1*x-20*y=1
- 14*x-10*y=-4
- -11*x+16*y=3
- Graphing y =:
- x^2-14*x+15
-
Identical expressions
- x^ two - fourteen *x+ fifteen = zero
- x squared minus 14 multiply by x plus 15 equally 0
- x to the power of two minus fourteen multiply by x plus fifteen equally zero
- x2-14*x+15=0
- x²-14*x+15=0
- x to the power of 2-14*x+15=0
- x^2-14x+15=0
- x2-14x+15=0
- x^2-14*x+15=O
-
Similar expressions
- x^2-14*x-15=0
- x^2+14*x+15=0
x^2-14*x+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
$$a = 1$$
$$b = -14$$
$$c = 15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{34} + 7$$
$$x_{2} = 7 - \sqrt{34}$$
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
$$a = 1$$
$$b = -14$$
$$c = 15$$
, then
D = b^2 - 4 * a * c =
(-14)^2 - 4 * (1) * (15) = 136
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{34} + 7$$
$$x_{2} = 7 - \sqrt{34}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -14$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 14$$
$$x_{1} x_{2} = 15$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -14$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 14$$
$$x_{1} x_{2} = 15$$
Sum and product of roots
[src]
sum
____ ____ 7 - \/ 34 + 7 + \/ 34
$$\left(7 - \sqrt{34}\right) + \left(\sqrt{34} + 7\right)$$
=
14
$$14$$
product
/ ____\ / ____\ \7 - \/ 34 /*\7 + \/ 34 /
$$\left(7 - \sqrt{34}\right) \left(\sqrt{34} + 7\right)$$
=
15
$$15$$
15
Rapid solution
[src]
____ x1 = 7 - \/ 34
$$x_{1} = 7 - \sqrt{34}$$
____ x2 = 7 + \/ 34
$$x_{2} = \sqrt{34} + 7$$
x2 = sqrt(34) + 7
The graph