If `sin alpha and cos alpha` are the roots of the equation `ax^(2)-bx-1=0`, then find the relation between a and b.

If `sin alpha and cos alpha` are the roots of the equation `ax^(2)-bx-

1.	If `sin alpha and cos alpha` are the roots of the equation `ax^(2)-bx-1=0`, then find the relation between a and b.
Answer» The given equation is `ax^(2)-bx-1=0`. Here, `a=a,b=-b and c=-1`. `sin alpha + cos alpha=(-b)/(a)=(-(-b))/(a)=(b)/(a)` `sin alpha * cos alpha=(c)/(a)=(-1)/(a)`. Consider, `sin alpha+ cos alpha=(-b)/(a)` Squaring on both sides, `(sin alpha+ cos alpha)^(2)=((-b)/(a))^(2)` `=1+2((-1)/(a))=(b^(2))/(a^(2))` `=1-(b^(2))/(a^(2))=(2)/(a)` `:. a^(2)-b^(2)=2a`