How do you find all the zeros of $F (x) = x^{2} + 10 x + 25$ $F(x)=x^2+10x+25$ ?

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Answer 1 · 2016-04-09T20:53:25

$x = - 5$ $x = -5$

Factorise the equation into

$(x + a) (x + b)$ $(x + a)(x + b)$

where $a + b = 10$ $a + b = 10$ and $a \cdot b = 25$ $a * b = 25$ . Using trial and error, this should give you $a = 5$ $a = 5$ and $b = 5$ $b = 5$ .

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

In order for this to be zero (i.e. to find the zeroes), $x + 5$ $x + 5$ must be zero, so

$x + 5 = 0$ $x + 5 = 0$
$x = - 5$ $x = -5$

How do you find all the zeros of F(x)=x2+10x+25F(x)=x^2+10x+25?