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Maru [420]
3 years ago
8

In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possible

Mathematics
1 answer:
baherus [9]3 years ago
8 0
To factor (x² +10x+24); you first have to ask yourself, what 2 numbers will multiply and give me positive 24, but add and give me positive 10? After listing your factors, (1,24)(2,12)(3,8)and (4,6); you decide that (4*6)=24 & adds to get you 10. Meaning that (x²+10x+24) factors are (x+4)(x+6). 
Now algebraically, there wouldn't be any other possible value of b, 6, because if you put (-6) & (4), those numbers will multiply and give you (-24) and add & give you (-2); & that is not what you're looking for. 

I hope I explained this enough for you to understand. (:
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Answer:

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Step-by-step explanation:

Let l,b denotes length and breadth of a rectangle.

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New length =l-6 inches

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Volume of box = length × breadth × height

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lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l

Put b=68-l in lb=1056

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At l=24,b=\frac{1056}{24}=44 inches

At l=44,b=\frac{1056}{44}=24 inches

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