Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4*x^4-5*x^2+1=0
-
Equation 5*x^2+7*x+2=0
-
Equation (x-4)^2-25=0
-
Equation (x+3)^4-4(x+3)^2-5=0
- Express {x} in terms of y where:
- -1*x+13*y=13
- 12*x+1*y=2
- -1*x+9*y=-1
- 1*x-11*y=-19
- Derivative of:
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(4x-3)^2
- Canonical form:
- (4x-3)^2
- Graphing y =:
- (4x-3)^2
-
Identical expressions
- (4x- three)^ two
- (4x minus 3) squared
- (4x minus three) to the power of two
- (4x-3)2
- 4x-32
- (4x-3)²
- (4x-3) to the power of 2
- 4x-3^2
-
Similar expressions
- (4x+3)^2
(4x-3)^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(4 x - 3\right)^{2} = 0$$
We get the quadratic equation
$$16 x^{2} - 24 x + 9 = 0$$
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
$$a = 16$$
$$b = -24$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{3}{4}$$
$$\left(4 x - 3\right)^{2} = 0$$
We get the quadratic equation
$$16 x^{2} - 24 x + 9 = 0$$
This equation is of the form
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
$$a = 16$$
$$b = -24$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-24)^2 - 4 * (16) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --24/2/(16)
$$x_{1} = \frac{3}{4}$$
Sum and product of roots
[src]
sum
3/4
$$\frac{3}{4}$$
=
3/4
$$\frac{3}{4}$$
product
3/4
$$\frac{3}{4}$$
=
3/4
$$\frac{3}{4}$$
3/4