[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: {p}^{2} - 10p + 7 = 0[/tex]
Now, let's use Quadratic formula :
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - ( - 10) \pm \sqrt{ {( - 10)}^{2} - 4(1 \times 7) } }{2 \times 1} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm \sqrt{ 100- 28 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm \sqrt{ 72 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 10 \pm6 \sqrt{ 2 } }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ 2(5 \pm3 \sqrt{ 2 }) }{2 } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = (5 \pm3 \sqrt{ 2 }) [/tex]
So, the required roots are :
[tex]\qquad \sf \dashrightarrow \:x = 5 + 3 \sqrt{ 2 } [/tex]
and
[tex]\qquad \sf \dashrightarrow \:x = 5 - 3 \sqrt{2} [/tex]
