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- Equation:
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Identical expressions
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Similar expressions
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(4x-3)(4x+3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(4 x - 3\right) \left(4 x + 3\right) = 0$$
We get the quadratic equation
$$16 x^{2} - 9 = 0$$
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
$$a = 16$$
$$b = 0$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{3}{4}$$
$$x_{2} = - \frac{3}{4}$$
$$\left(4 x - 3\right) \left(4 x + 3\right) = 0$$
We get the quadratic equation
$$16 x^{2} - 9 = 0$$
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
$$a = 16$$
$$b = 0$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (16) * (-9) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{3}{4}$$
$$x_{2} = - \frac{3}{4}$$
Sum and product of roots
[src]
sum
-3/4 + 3/4
$$- \frac{3}{4} + \frac{3}{4}$$
=
0
$$0$$
product
-3*3 ---- 4*4
$$- \frac{9}{16}$$
=
-9/16
$$- \frac{9}{16}$$
-9/16