Answer:
Ques 1: ![-1\pm2i](https://tex.z-dn.net/?f=-1%5Cpm2i)
Ques 2: ![(3x+5)](https://tex.z-dn.net/?f=%283x%2B5%29)
Step-by-step explanation:
<em>The quadratic formula states that the roots of the equation,
are given by,
.</em>
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}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%20%5Csqrt%7B6%5E2-4%5Ctimes%203%5Ctimes%2015%7D%7D%7B2%5Ctimes%203%7D)
i.e. ![x=\frac{-6\pm \sqrt{36-180}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%20%5Csqrt%7B36-180%7D%7D%7B6%7D)
i.e. ![x=\frac{-6\pm \sqrt{-144}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%20%5Csqrt%7B-144%7D%7D%7B6%7D)
i.e. ![x=\frac{-6\pm 12i}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%2012i%7D%7B6%7D)
i.e.
and i.e. ![x=\frac{-6-12i}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6-12i%7D%7B6%7D)
i.e.
and i.e. ![x=-1-2i](https://tex.z-dn.net/?f=x%3D-1-2i)
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}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-21%5Cpm%20%5Csqrt%7B21%5E2-4%5Ctimes%209%5Ctimes%2010%7D%7D%7B2%5Ctimes%209%7D)
i.e. ![x=\frac{-21\pm \sqrt{441-360}}{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-21%5Cpm%20%5Csqrt%7B441-360%7D%7D%7B18%7D)
i.e. ![x=\frac{-21\pm \sqrt{81}}{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-21%5Cpm%20%5Csqrt%7B81%7D%7D%7B18%7D)
i.e. ![x=\frac{-21\pm 9}{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-21%5Cpm%209%7D%7B18%7D)
i.e.
and i.e. ![x=\frac{-21-9}{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-21-9%7D%7B18%7D)
i.e.
and i.e. ![x=\frac{-30}{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-30%7D%7B18%7D)
i.e.
and i.e. ![x=\frac{-5}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-5%7D%7B3%7D)
That is, the factors are
and ![(3x+5)](https://tex.z-dn.net/?f=%283x%2B5%29)
So, according to the options,
is the correct option.