Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x^4-17x^2+16=0
- Equation 2x^2-50=0
-
Equation x^4+2x^2-8=0
-
Equation 16x^2-8x+1=0
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 4*x-16*y=6
- 5*x+5*y=20
-
Identical expressions
- one 6x^ two -8x+1= zero
- 16x squared minus 8x plus 1 equally 0
- one 6x to the power of two minus 8x plus 1 equally zero
- 16x2-8x+1=0
- 16x²-8x+1=0
- 16x to the power of 2-8x+1=0
- 16x^2-8x+1=O
-
Similar expressions
- 16x^2-8x-1=0
- 16x^2+8x+1=0
16x^2-8x+1=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
$$a = 16$$
$$b = -8$$
$$c = 1$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{1}{4}$$
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
$$a = 16$$
$$b = -8$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (16) * (1) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --8/2/(16)
$$x_{1} = \frac{1}{4}$$
Vieta's Theorem
rewrite the equation
$$16 x^{2} - 8 x + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{2} + \frac{1}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{2}$$
$$x_{1} x_{2} = \frac{1}{16}$$
$$16 x^{2} - 8 x + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{2} + \frac{1}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{2}$$
$$x_{1} x_{2} = \frac{1}{16}$$
Sum and product of roots
[src]
sum
0 + 1/4
$$0 + \frac{1}{4}$$
=
1/4
$$\frac{1}{4}$$
product
1*1/4
$$1 \cdot \frac{1}{4}$$
=
1/4
$$\frac{1}{4}$$
1/4
The graph