Question

There are a total of 2x^2 – 3x – 35 students. These students are to be
arranged in rows and columns during the assembly. Find the number of
rows of columns to be arranged?

Answer 1

19

Step-by-step explanation:

2x^2-3x-35=0

2x^2-3x=35

2x^2-x=35+3

=38

2x=38

x=38/2

x=19

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Answer 2

The number of rows and columns are (2x+7) and (x-5).

Step-by-step explanation:

Given, total number of students =  $2x^{2}-3x-35$

Now, we have to arrange these students in rows and columns during the assembly, which simply means, we have to factorise the total number of students, such that the two factors come out to be rows and columns respectively.

So, lets factorise $2x^{2}-3x-35$.

Now, since $2 \times 35 =70$, so we have to factorise 70 in such a way that the factors subtract to give -3.

And $70=7 \times 10$.

also, $7-10=-3$

So, $2x^{2}-3x-35 = 2x^{2}-10x+7x-35$

                            $= 2x(x-5)+7(x-5)\\=(2x+7)(x-5)$ [ Taking common using distributivity ]

Hence, the number of rows and columns are (2x+7) and (x-5).