Does the polynomial a4 + 4a2 + 5 = 0 have real zeroes?
Answers
Answer:
Step-by-step explanation:
tep-by-step explanation:
a4-4a2plus 5
Final result :
(a2 + 4) • (a + 3) • (a - 3)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((a4) - 5a2) - 36
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring a4-5a2-36
The first term is, a4 its coefficient is 1 .
The middle term is, -5a2 its coefficient is -5 .
The last term, "the constant", is -36
Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
a4 - 9a2 + 4a2 - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
a2 • (a2-9)
Add up the last 2 terms, pulling out common factors :
4 • (a2-9)
Step-5 : Add up the four terms of step 4 :
(a2+4) • (a2-9)