Question

Solve: p^2-12p+21. Maths Question

Answer 1

Apply the quadratic equation to gain the roots.

that is
$a = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}$
and

$\beta = \frac{ - b - \sqrt{ {b }^{2} - 4ac} }{2a}$

Now in the given equation,

a = 1 , b = -12 and c = 21

Substitute these values in the quadratic equation

$\alpha = \frac{ - ( -12) + \sqrt{ {( - 12)}^{2} - 4(1)(21)} }{2(1)} \\ = \frac{12 + \sqrt{144 - 84} }{2} \\ = \frac{12 + \sqrt{60} }{2 } \\ \\ \frac{12 + 2 \sqrt{15} }{2}$


= 6 + √15


Similarly,
the other root will be
$\frac{12 - 2 \sqrt{15} }{2}$


= 6 -√15