Question

36x4 - 60x3 +61x2 -mx +n​

Answer 1

★Question★

To determine

The value of m and n such that the below polynomial is a perfect square

36x⁴ - 60x³ + 61x² - mx + n

Answer:-

36x⁴ - 60x³ + 61x² - mx + n

= (6x²)² - 2.6x².5x + (5x)² + 36x² - mx + n

= (6x² - 5x)² + 36x² - mx + n

= (6x² - 5x)² + 2.3.(6x² - 5x) + 30x - mx + n

= (6x² - 5x)² + 2.3.(6x² - 5x) + 3² + (30 - m)x

= (6x² - 5x + 3)² + (30 - m)x + (n - 9)

Therefore the last obtained polynomial will be a perfect square if

30 - m = 0 and n - 9 = 0

Now

30 - m = 0 gives m = 30

n - 9 = 0 gives n = 9

Final result

The required value of m and n are 30 and 9 respectively such that the below polynomial is a perfect square

36x⁴ - 60x³ + 61x² - mx + n

@BengaliBeauty

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