Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 49*x^3+14*x^2+x=0
-
Equation 4^x=8
-
Equation x^2-x=12
-
Equation x-5(x+3)=5
- Express {x} in terms of y where:
- -7*x-13*y=-12
- -3*x+19*y=16
- -4*x+4*y=-9
- -19*x-2*y=-6
-
Identical expressions
- x^ two - fourteen *x- fifteen = zero
- x squared minus 14 multiply by x minus 15 equally 0
- x to the power of two minus fourteen multiply by x minus 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
$$x_{1} = 15$$
$$x_{2} = -1$$
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) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 15$$
$$x_{2} = -1$$
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
-1 + 15
$$-1 + 15$$
=
14
$$14$$
product
-15
$$- 15$$
=
-15
$$-15$$
-15