Question

Hi Guys!

Question :

What must be added to x^2 + 10x +23 to make it a perfect square?

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#Please answer it Please...

Answer 1

Answer:

2

when we add two in this polynomial we get a perfect square as

${x}^{2} + 10x + 23 + 2 \\ = {x}^{2} + 10x + 25 \\ = {(x + 5)}^{2}$

Explanation:-

Let us firstly assume that the given polynomial is only

${x}^{2} + 10x + 0$

now to make it perfect square we have

do to add

${( \frac{ {coefficient \: of \: x} }{2 \times coefficient \: of \: {x}^{2} })}^{2}$

as

${x}^{2} + 10x + {( \frac{10}{2 \times 1} )}^{2} \\ = {x}^{2} + 10x + {( \frac{10}{2} )}^{2} \\ = {x}^{2} + 10x + {5}^{2} \\ = {x}^{2} + 10x + 25$

$will \: be \: a \: perfect \: square \: as \\ {(x + 5)}^{2} </p><p>$

now as given polynomial is

${x}^{2} + 10x + 23$

so we have to add only 2 to make 23 as 25

so it will become a perfect square as

${(x + 5)}^{2}$