Ques 1: ![-1\pm2i](/tpl/images/0218/3056/d628f.png)
Ques 2: ![(3x+5)](/tpl/images/0218/3056/87100.png)
Step-by-step explanation:
The quadratic formula states that the roots of the equation,
are given by,
.
Ques 1: The quadratic equation is given by,
.
On comparing, a= 3, b= 6 and c= 15.
So, the roots of the equation are given by,
![x=\frac{-6\pm \sqrt{6^2-4\times 3\times 15}}{2\times 3}](/tpl/images/0218/3056/0715b.png)
i.e. ![x=\frac{-6\pm \sqrt{36-180}}{6}](/tpl/images/0218/3056/82a4e.png)
i.e. ![x=\frac{-6\pm \sqrt{-144}}{6}](/tpl/images/0218/3056/31f86.png)
i.e. ![x=\frac{-6\pm 12i}{6}](/tpl/images/0218/3056/b94bc.png)
i.e.
and i.e. ![x=\frac{-6-12i}{6}](/tpl/images/0218/3056/9a652.png)
i.e.
and i.e. ![x=-1-2i](/tpl/images/0218/3056/d83f4.png)
Thus, the solutions of the equation are
.
Ques 2: The quadratic equation is
.
On comparing, a= 9, b= 21 and c= 10.
So, the roots of the equation are given by,
![x=\frac{-21\pm \sqrt{21^2-4\times 9\times 10}}{2\times 9}](/tpl/images/0218/3056/e4d63.png)
i.e. ![x=\frac{-21\pm \sqrt{441-360}}{18}](/tpl/images/0218/3056/1c330.png)
i.e. ![x=\frac{-21\pm \sqrt{81}}{18}](/tpl/images/0218/3056/52076.png)
i.e. ![x=\frac{-21\pm 9}{18}](/tpl/images/0218/3056/ee065.png)
i.e.
and i.e. ![x=\frac{-21-9}{18}](/tpl/images/0218/3056/eb1a9.png)
i.e.
and i.e. ![x=\frac{-30}{18}](/tpl/images/0218/3056/10063.png)
i.e.
and i.e. ![x=\frac{-5}{3}](/tpl/images/0218/3056/9142e.png)
That is, the factors are
and ![(3x+5)](/tpl/images/0218/3056/87100.png)
So, according to the options,
is the correct option.