For all you math whizzes! Must the sum of 2 second-degree polynomials be a second degree polynomial?

Question

Must the sum of 2 second-degree polynomials be a second degree polynomial? Explain your answer with examples. Thank you.

Answer 1

No.
Let P(x) = x^2 + x and let R(x) = -x^2 + x, then
P(x) + R(x) = x^2 + x - x^2 + x
= 2x
which is a first degree polynomial

Answer 2

Given the quartic polynomial equation x^4 - 5x² + 4 = 0 because the equation is quartic (degree 4), then evidently it has 4 thoughts. This equation is a particular case of the more effective wide-spread quartic kind ax^4 + bx³ + cx² + dx + e = 0 the position b = 0 and d = 0. it really is particular because it should be solved extremely making use of quadratic methods. One is through substituting yet another variable (say z). allow z = x² therefore, z² = x^4. x^4 - 5x² + 4 = 0 change z² - 5z + 4 = 0 ingredient, (z - 4)(z - a million) = 0 for this reason, z = 4 or z = a million. We change again z = x² x² = 4 or x² = a million therefore, the "4" thoughts are x = 2,x = -2,x = a million or x = -a million. -------------------------------- regardless of each and every thing, the equation should be factored as x^4 - 5x² + 4 = 0 (x² - 4)(x² - a million) = 0 (x - 2)(x + 2)(x - a million)(x + a million) = 0 so that you get the 4 thoughts. i desire you get it!!!!! ^_^

Answer 3

the sum of two polynomials wont produce an answer with a higher degree polynomial (a,b,c,d,e,f all real numbers)

ax^2 + bx +c

dx^2 +ex + f

if you know that a =-d (etc) then you will get a lower degree answer

but whatever means you employ you wont get a higher degree polynomial for an answer

Answer 4

Yes if you ADD two positive 2nd degree, but as you see in Mathgal answer, NO if you add the opposite.