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chloedonyes
28.10.2019 •
Mathematics
Find all solutions to the following quadratic equations, and write each equation in factored form.
a. x^2 + 25 = 0
b. −x^2 − 16 = −7
c. (x + 2)^2 + 1 = 0
d. (x + 2)^2 = x
e. (x^2 + 1)^2 + 2(x^2 + 1) − 8 = 0
f. (2x − 1)^2 = (x + 1)^2 − 3
g. x^3 + x^2 − 2x = 0
h. x^3 − 2x^2 + 4x − 8 = 0
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Ответ:
(a) The solutions are:![x=5i,\:x=-5i](/tpl/images/0349/8120/b4bcb.png)
(b) The solutions are:![x=3i,\:x=-3i](/tpl/images/0349/8120/10d10.png)
(c) The solutions are:![x=i-2,\:x=-i-2](/tpl/images/0349/8120/29514.png)
(d) The solutions are:![x=-\frac{3}{2}+i\frac{\sqrt{7}}{2},\:x=-\frac{3}{2}-i\frac{\sqrt{7}}{2}](/tpl/images/0349/8120/250dd.png)
(e) The solutions are:![x=1,\:x=-1,\:x=\sqrt{5}i,\:x=-\sqrt{5}i](/tpl/images/0349/8120/1574a.png)
(f) The solutions are:![x=1](/tpl/images/0349/8120/dd2c7.png)
(g) The solutions are:![x=0,\:x=1,\:x=-2](/tpl/images/0349/8120/28f08.png)
(h) The solutions are:![x=2,\:x=2i,\:x=-2i](/tpl/images/0349/8120/fc9d1.png)
Step-by-step explanation:
To find the solutions of these quadratic equations you must:
(a) For![x^2+25=0](/tpl/images/0349/8120/a7962.png)
The solutions are:![x=5i,\:x=-5i](/tpl/images/0349/8120/b4bcb.png)
(b) For![-x^2-16=-7](/tpl/images/0349/8120/4e84a.png)
The solutions are:![x=3i,\:x=-3i](/tpl/images/0349/8120/10d10.png)
(c) For![\left(x+2\right)^2+1=0](/tpl/images/0349/8120/f2f59.png)
The solutions are:![x=i-2,\:x=-i-2](/tpl/images/0349/8120/29514.png)
(d) For![\left(x+2\right)^2=x](/tpl/images/0349/8120/fa18c.png)
For a quadratic equation of the form
the solutions are:
The solutions are:![x=-\frac{3}{2}+i\frac{\sqrt{7}}{2},\:x=-\frac{3}{2}-i\frac{\sqrt{7}}{2}](/tpl/images/0349/8120/250dd.png)
(e) For![\left(x^2+1\right)^2+2\left(x^2+1\right)-8=0](/tpl/images/0349/8120/a7d10.png)
The solutions are:![x=1,\:x=-1,\:x=\sqrt{5}i,\:x=-\sqrt{5}i](/tpl/images/0349/8120/1574a.png)
(f) For![\left(2x-1\right)^2=\left(x+1\right)^2-3](/tpl/images/0349/8120/bd046.png)
The solutions are:![x=1](/tpl/images/0349/8120/dd2c7.png)
(g) For![x^3+x^2-2x=0](/tpl/images/0349/8120/cc3af.png)
Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0
The solutions are:![x=0,\:x=1,\:x=-2](/tpl/images/0349/8120/28f08.png)
(h) For![x^3-2x^2+4x-8=0](/tpl/images/0349/8120/732dc.png)
Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0
The solutions are:![x=2,\:x=2i,\:x=-2i](/tpl/images/0349/8120/fc9d1.png)
Ответ: