Is it possible to factor $y=x^2+5x-3$ ? If so, what are the factors?

Question

6050 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-09T12:22:33

Factors are $(x+5/2-sqrt37/2)(x+5/2+sqrt37/2)$

In $y=x^2+5x-3$ , the discriminant is given by $5^2-4*1*(-3)=25+12=37$ , which is positive but not a square of a rational number.

Hence, we can have irrational factors of $y=x^2+5x-3$ .

As roots of $x^2+5x-3=0$ are $x=(-5+-sqrt37)/2$

or $x=-5/2+sqrt37/2$ and $x=-5/2-sqrt37/2$

Hence factors of $y=x^2+5x-3$ are

$(x-(-5/2+sqrt37/2))(x-(-5/2-sqrt37/2))$ or

$(x+5/2-sqrt37/2)(x+5/2+sqrt37/2)$

Is it possible to factor y=x^2+5x-3 y=x^2+5x-3 ? If so, what are the factors?