Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x+5=0
-
Equation 4*x^2-25=0
-
Equation 8x-15=-12+5x
- Express {x} in terms of y where:
- -14*x+16*y=6
- -4*x-15*y=6
- 8*x-6*y=-18
- -5*x-14*y=18
-
Identical expressions
- x^ two + nine *x+ fourteen = zero
- x squared plus 9 multiply by x plus 14 equally 0
- x to the power of two plus nine multiply by x plus fourteen equally zero
- x2+9*x+14=0
- x²+9*x+14=0
- x to the power of 2+9*x+14=0
- x^2+9x+14=0
- x2+9x+14=0
- x^2+9*x+14=O
-
Similar expressions
- x^2+9*x-14=0
- x^2-9*x+14=0
x^2+9*x+14=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
$$a = 1$$
$$b = 9$$
$$c = 14$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -7$$
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
$$a = 1$$
$$b = 9$$
$$c = 14$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (1) * (14) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -7$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 9$$
$$q = \frac{c}{a}$$
$$q = 14$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -9$$
$$x_{1} x_{2} = 14$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 9$$
$$q = \frac{c}{a}$$
$$q = 14$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -9$$
$$x_{1} x_{2} = 14$$
Sum and product of roots
[src]
sum
-7 - 2
$$-7 - 2$$
=
-9
$$-9$$
product
-7*(-2)
$$- -14$$
=
14
$$14$$
14
The graph