Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 6*x^2+x-7=0
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Equation (x^2-9)^2+(x^2+x-6)^2=0
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Equation (x-5)=(x+10)^2
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Equation x^3+4*x^2+x-6=0
- Express {x} in terms of y where:
- 2*x+20*y=16
- -15*x-12*y=17
- -20*x+5*y=-11
- 2*x+10*y=-5
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Identical expressions
- x^ two - fourteen *x- five = zero
- x squared minus 14 multiply by x minus 5 equally 0
- x to the power of two minus fourteen multiply by x minus five equally zero
- x2-14*x-5=0
- x²-14*x-5=0
- x to the power of 2-14*x-5=0
- x^2-14x-5=0
- x2-14x-5=0
- x^2-14*x-5=O
-
Similar expressions
- x^2+14*x-5=0
- x^2-14*x+5=0
x^2-14*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
$$a = 1$$
$$b = -14$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7 + 3 \sqrt{6}$$
$$x_{2} = 7 - 3 \sqrt{6}$$
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
$$a = 1$$
$$b = -14$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(-14)^2 - 4 * (1) * (-5) = 216
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7 + 3 \sqrt{6}$$
$$x_{2} = 7 - 3 \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -14$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 14$$
$$x_{1} x_{2} = -5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -14$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 14$$
$$x_{1} x_{2} = -5$$
Rapid solution
[src]
___ x1 = 7 - 3*\/ 6
$$x_{1} = 7 - 3 \sqrt{6}$$
___ x2 = 7 + 3*\/ 6
$$x_{2} = 7 + 3 \sqrt{6}$$
x2 = 7 + 3*sqrt(6)
Sum and product of roots
[src]
sum
___ ___ 7 - 3*\/ 6 + 7 + 3*\/ 6
$$\left(7 - 3 \sqrt{6}\right) + \left(7 + 3 \sqrt{6}\right)$$
=
14
$$14$$
product
/ ___\ / ___\ \7 - 3*\/ 6 /*\7 + 3*\/ 6 /
$$\left(7 - 3 \sqrt{6}\right) \left(7 + 3 \sqrt{6}\right)$$
=
-5
$$-5$$
-5