Solve X^4+9X^2=-20?

Answer 1

X^4+9X^2=-20
Let t = x^2, t > 0 to turn it into a quadratic equation:

t^2 + 9t = -20
t^2 + 9t + 20 = 0
=> t1 = (9+1)/2 = 5
t2 = (9-1)/2 = 4

=> x1 = sqrt(t1) = sqrt(5)
x2 = -sqrt(t1) = -sqrt(5)
x3 = sqrt(t2) = 2
x4 = -sqrt(t2) = -2

Answer 2

x^4 + 9x^2 = -20
= x^4 +9x^2 +20 =0
this is a quadratic eq,
= x^4 + 5x^2 + 4x^2 +20 =0
=x^2(x^2 + 5) + 4(x^2 + 5) =0
= (x^2 + 4) (x^2 +5) =0
either x^2 + 4 =0 or x^2 + 5 = 0
x^2 = -4 or x^2 = -5
x = -2 or x = root -5
so answer is x = -2

Answer 3

if you are trying to factor this...
add 20 to both sides... leaving the right side to equal zero
then the problem would be
x^4+9x^2+20=0
use the magic x or spliting the middle term if you know how
find 2 multiples that mulitiply to 20 but add up to 9
so your answer should be
(x^2 +4)(x^2+5)
if your trying to solve for x
use the zero products property
so it is
x^2 + 4 = 0 or x^2+5=0
then you solve for x

Answer 4

X^4 + 9X^2 = -20
X^4 + 9X^2 + 20 = 0
(X^2 + 5)(X^2 + 4) = 0
X^2 = -5 or X^2 = -4

Since i^2 = -1,

X^2 = 5i^2

X^2 = 4i^2

and since for square root, you'll get + and -,

X = +(square root 5)i or = - (square root 5)i
X = +(square root 4)i or = -(square root 4)i

Answer 5

according to question

x^4+9x^2=-20
let we consider x^2=y
then
y^2+9=-20
y^2=-20-9
y^2=-29
put the value of y in this equation
then
x=-29answer

Answer 6

I'll show you how to do the first 8, but I got tired after that! Nobody is going to do ALL of your homework for you. I will show you how to do these an easy way, and after that you should be able to work the remaining problems yourself. 1) Question 1 (True/False Worth 5 points) 4x2 - 12x + 9 can be factored as (2x - 3)(2x - 3) Answer: I set up my factors like I am working long division. I will use dots to properly space things visually because Yahoo Answers removes spaces. ...............2X - 3 ...............2X - 3 ...............---------- ..............-6X - 9 .......4X2 - 6X .......------------------- .......4X2 - 12X - 9 First multiply the minus three on the second line by the minus three and the 2X on the first line, like you would multiply the first digit of the second number by each of the numbers in the first number in long division. Then multiply the 2X of the second line by the -3 and the 2X of the first line. Now add your like terms. You can see that when those two factors are multiplied, you do indeed get 4X2 - 12X + 9, so the answer is true. 2) What is the Greatest Common Factor for the given polynomial? 5x3y2 + 15xy2 + 25x2y3 a) 5x b) 5xy c) 5xy2 d) prime Answer: I usually start by looking at the numbers in front. What do 5, 15 and 25 all have in common? They are each divisible by 5. So, first divide everything in your equation by 5, and you are left with: X3Y2 + 3XY2 + 5X2Y3 Now look at the Xs in each term. How many can you divide out? Because the second term only has one X, you can't divide by more than that. So divide the whole thing by X, and you have this left: X2Y2 + 3Y2 + 5XY3 Now look at the Ys and see how many you can divide out. Each term has at LEAST a Y2, so you can divide that out, leaving: X2 + 3 + 5XY OK, so that is your final expression. What terms did we divide by? Put them together. They were 5, X, and Y2, so our factor was 5XY2, which matches the third answer (answer c). Therefore, the final answer is 5XY2(X2 + 3 + 5XY) 3) Factor completely: 8x4 + 4x3 - 24x2 a) 4x2(2x2 + x – 6) b) 4x2(2x – 3)(x + 2) c) 4(2x4 + x3 - 6x2) prime Answer: What do 8, 4 and 24 have in common? The four. Divide it out. 2X4 + X3 - 6X2 What's the lowest term of X in the above? X2, so divide it out. 2X2 + X - 6 That's our final expression (there are no Ys). What did we divide out? A four and an X2. So, the answer is 4X2(2X2 + X - 6), which matches the first answer (answer a). 4) Factor completely: 5x4 - 125 a) 5(x4 - 25) b) 5(x2 + 5)(x2 - 5) c) 5(x2 + 5)(x – 3)(x – 2) d) prime Answer: Start out as before: What number do 5 and 25 have in common? The answer is 5, so divide that out. We're left with: X4 - 25 You could stop there, but you notice that it's possible to take a square root of each of those terms? X2 and 5 would yield X4 and 25. But how would you work it so that you get the MINUS 25 and also NO X2's in the final answer? The answer is to have one -5 and one +5, and then the middle terms will cancel each other out: Again, set it up like long division to see that this is true. ....................X2 + 5 ....................X2 - 5 ....................---------- ....................-5X2 - 25 .............X4 + 5X2 .............----------------------- .............X4...........- 25 We have verified that (X2 + 5)(X2 - 5) works, so combine that with the 5 that we divided out in the beginning, and we get 5(X2 = 5)(X2 - 5), which matches answer b above. 5) Question 5 (Multiple Choice Worth 1 points) Factor: x2 - 12x + 36 Which of the following is one of the factors? a) (x - 6) b) (x + 9) c) (x – 4) Answer: There are no common terms to divide by, we see. We want to find what two numbers, when multiplied together, will equal +36, and will also, when added together, give -12. The answer is -8 and -4. And what two products equal X2? X of course. Now let's put those together and see if it works: ....................X - 8 ....................X - 4 ....................-------- .................-4X - 32 ............X2 - 8X ............------------------ ............X2 - 12X -32 So the two factors are (X - 8) and (X - 4). The second one matches answer c. 6) Question 6 (Fill-In-The-Blank Worth 5 points) x2 - 9x + 18 = 0 Solve for x. x = ____? and x = _____? Place only the number in the space provided. Place the smaller number in the first blank and the larger number in the second blank. Numerical Answers Expected! Answer for Blank 1: Answer for Blank 2: Basically, you are being asked to factor X2 - 9X + 18, and then solve for X in the two factors. First, what two numbers, when multiplied together, give +18, and also, when added together, give -9? The answer is -6 and -3. And what is the square root of X2? X of course. So let's try it: .....................X - 6 .....................X - 3 ..................

Answer 7

==> X^4+9X^2+20=0
let X^2=y
=> Y^2+9Y+20=0
=>(Y-4)(Y-5)=0
=>Y=4 OR Y=5
=>X^2 = 4 OR 5
therefore X=+2 or -2 or +root5 or -root5

Answer 8

use the quadratic formula, except instead of solving for x = solve for x^2 =
x^2 = (-9 +- (81 - 4(1)(20))^.5)/2
x^2 = -5,-4
x = 5i,-5i,4i,-4i

to the answer above
(y-4)(y-5) = y^2 - 9y + 20, should be (y+4)(y+5)

Answer 9

Let x^2= Y

Y^2+9Y=-20
Y^2+9Y+20=0
(Y+4)(Y+5)=0

Therefore Y=-4,-5
and X^2=4, -5
Since -5 cannot be rooted.
X^2=4
X= +/-2
X= 2, -2

Answer 10

x^4+9x^2+20=0

(x^2+4)(x^2+5)=0

x^2=-4
x^2=-5

x=4i,-4i,5i,-5i