Question

if p and q are zeros of 3x'2 +2x -9, then the value of p - q is

Answer 1

Answer:

p - q =

$\frac{4\sqrt{7} }{3} .$

Step-by-step explanation:

$p + q = \frac{ - 2}{3} \\ \\ pq = \frac{ - 9}{3} = - 3 \\ \\ {(p - q)}^{2} = {(p + q)}^{2} - 4pq \\ \\ then \: \: \: \: p - q = \sqrt{ {(p + q)}^{2} - 4pq } \\ \\ = \sqrt{ {( \frac{2}{3} )}^{2} - 4( - 3) } \\ \\ = \sqrt{ \frac{4 + 108}{9} } \\ \\ = \sqrt{ \frac{112}{9 } } \\ \\ = \frac{2 \sqrt{28} }{3} \\ \\ = \frac{4 \sqrt{7} }{3}$