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kirill115 [55]
3 years ago
8

HELP ASAP : Find the largest value of n such that 5x^2+nx+48 can be factored as the product of two linear factors with integer c

oefficients
Mathematics
1 answer:
Anna71 [15]3 years ago
7 0

Answer:

n=241

Step-by-step explanation:

We are given

5x^2+nx+48

Let's assume it can be factored as

5x^2+nx+48=(5x-s)(x-r)

now, we can multiply right side

and then we can compare it

5x^2+nx+48=5x^2-5rx-sx+rs

5x^2+nx+48=5x^2-(5r+s)x+rs

now, we can compare coefficients

rs=48

5r+s=-n

n=-(5r+s)

now, we can find all possible factors of 48

and then we can assume possible prime factors of 48

48=-+(1\times 48)

48=-+(2\times 24)

48=-+(3\times 16)

48=-+(4\times 12)

48=-+(6\times 8)

Since, we have to find the largest value of n

So, we will get consider larger value of r because of 5r

and because n is negative of 5r+s

so, we will both n and r as negative

So, we can assume

r=-48 and s=-1

so, we get

n=-(5\times -48-1)

n=241


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