Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2=18*x
-
Equation 16*x^2-9=0
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Equation 0*x=5
- Equation x^2-16*x+4=0
- Express {x} in terms of y where:
- 10*x-18*y=-6
- 3*x-12*y=-14
- 16*x+11*y=-14
- -4*x+20*y=-14
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Identical expressions
- x^ two - sixteen *x+ four = zero
- x squared minus 16 multiply by x plus 4 equally 0
- x to the power of two minus sixteen multiply by x plus four equally zero
- x2-16*x+4=0
- x²-16*x+4=0
- x to the power of 2-16*x+4=0
- x^2-16x+4=0
- x2-16x+4=0
- x^2-16*x+4=O
-
Similar expressions
- x^2-16*x-4=0
- x^2+16*x+4=0
x^2-16*x+4=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
$$a = 1$$
$$b = -16$$
$$c = 4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2 \sqrt{15} + 8$$
$$x_{2} = 8 - 2 \sqrt{15}$$
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
$$a = 1$$
$$b = -16$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(-16)^2 - 4 * (1) * (4) = 240
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{15} + 8$$
$$x_{2} = 8 - 2 \sqrt{15}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -16$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 16$$
$$x_{1} x_{2} = 4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -16$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 16$$
$$x_{1} x_{2} = 4$$
Sum and product of roots
[src]
sum
____ ____ 8 - 2*\/ 15 + 8 + 2*\/ 15
$$\left(8 - 2 \sqrt{15}\right) + \left(2 \sqrt{15} + 8\right)$$
=
16
$$16$$
product
/ ____\ / ____\ \8 - 2*\/ 15 /*\8 + 2*\/ 15 /
$$\left(8 - 2 \sqrt{15}\right) \left(2 \sqrt{15} + 8\right)$$
=
4
$$4$$
4
Rapid solution
[src]
____ x1 = 8 - 2*\/ 15
$$x_{1} = 8 - 2 \sqrt{15}$$
____ x2 = 8 + 2*\/ 15
$$x_{2} = 2 \sqrt{15} + 8$$
x2 = 2*sqrt(15) + 8