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- Equation:
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Equation x^3+4=0
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Equation 15-16x+4x^2=0
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Identical expressions
- fifteen -16x+4x^ two = zero
- 15 minus 16x plus 4x squared equally 0
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Similar expressions
- 15-16x-4x^2=0
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15-16x+4x^2=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
$$a = 4$$
$$b = -16$$
$$c = 15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = \frac{3}{2}$$
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
$$a = 4$$
$$b = -16$$
$$c = 15$$
, then
D = b^2 - 4 * a * c =
(-16)^2 - 4 * (4) * (15) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = \frac{3}{2}$$
Vieta's Theorem
rewrite the equation
$$4 x^{2} + \left(15 - 16 x\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x + \frac{15}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = \frac{15}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = \frac{15}{4}$$
$$4 x^{2} + \left(15 - 16 x\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x + \frac{15}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = \frac{15}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = \frac{15}{4}$$
Sum and product of roots
[src]
sum
3/2 + 5/2
$$\frac{3}{2} + \frac{5}{2}$$
=
4
$$4$$
product
3*5 --- 2*2
$$\frac{3 \cdot 5}{2 \cdot 2}$$
=
15/4
$$\frac{15}{4}$$
15/4
The graph