Question

find the values of m and n if the following polynomial are perfect squares 36x⁴-60x³+61x²-mx+n

Answer 1

Step-by-step explanation:

using long division method

m= -30 , n = 9

Answer 2

Answer: The value of m is -30 and n is 9

Step-by-step explanation:

Step 1: Using the long division method

The equation is $36x^4-60x^3+61x^2-mx+n$

$6x^2\hspace{40}\sqrt{36x^4-60x^3+61x^2-mx+n}/6x^2-5x+6\\.\hspace{60}36x^4\\12x^2-5x|\hspace{38} -60x^3+61x^2\\.\hspace{80}-60x^3-25x^2\\\\.12x^2-10x+3|\hspace{58}36x^2-mx+n\\.\hspace{125}36x^2-30x+9\\.\hspace{145}-m+30 \hspace{10} n-9$

Step 2: For a perfect square

The reminder should be equal to 0

Therefore, m = -30 and n = 9