How can you quickly find out that -64 and -36 are the numbers that add up to -100 and multiply to 2304?. Created by Edwin. science-mathematics-en - mathematics-en

What is a quick way to find that ℓ⁴ - 100ℓ² + 2304 = 0 is equal to (ℓ² - 64)(ℓ²

Edwin @Edwin

May 2021 3 144 Report

What is a quick way to find that ℓ⁴ - 100ℓ² + 2304 = 0 is equal to (ℓ² - 64)(ℓ² - 36) = 0?

How can you quickly find out that -64 and -36 are the numbers that add up to -100 and multiply to 2304?

Science & Mathematics / Mathematics

Verified answer

Use the quadratic formula. No guessing.

Let x = ℓ², then the equation becomes

x² - 100x + 2304 = 0

quadratic formula

x = [100 ± √(100² – 4·1·2304)] / [2·1]

= [100 ± √784] / 2

= [100 ± 28] /2

= 36, 64

x² - 100x + 2304 = (x - 64)(x - 36)

= (ℓ² - 64) (ℓ² - 36)

= (ℓ+8)(ℓ-8) (ℓ+6)(ℓ-6)

ted s

Hmmm..FAST...doubt it....you know they can't be 50 & 50 as that becomes 2500 and 40 x 60 = 2400 ..still too large while 30 x 70 = 2100 which is too small...furthermore the numbers either both end in 2 or end in 6 & 4 since the last digit is a 4.....so 32 , 34 , or 36...but 32 ---> 68 and that product ends in 6....34 & 66 or 36 and 64