Find the roots of the following quadratic equation by factorisation:
$x^{2}-3x-10=0$
$x^{2}-3x-10=0$
(A) To find the roots of the quadratic equation $x^{2}-3x-10=0$ by factorisation,we split the middle term.
We need two numbers whose product is $-10$ and whose sum is $-3$. These numbers are $-5$ and $2$.
$x^{2}-5x+2x-10=0$
Factor by grouping:
$x(x-5)+2(x-5)=0$
$(x-5)(x+2)=0$
Setting each factor to zero:
$x-5=0$ or $x+2=0$
Therefore,the roots are $x=5$ or $x=-2$.
We need two numbers whose product is $-10$ and whose sum is $-3$. These numbers are $-5$ and $2$.
$x^{2}-5x+2x-10=0$
Factor by grouping:
$x(x-5)+2(x-5)=0$
$(x-5)(x+2)=0$
Setting each factor to zero:
$x-5=0$ or $x+2=0$
Therefore,the roots are $x=5$ or $x=-2$.
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