Question

If m and n are zeroes of the polynomial p(x)=x2 -4x-5 then find the value of m^2 +n^2 and m ^-1 +n^-1

Answer 1

Answer:

Since m and n are zeroes of p(x).

$m + n = \frac{ - b}{a} \: and \: mn = \frac{c}{a}$

Now,

$p(x) = {x}^{2} - 4x - 5$

Here, a=1,b=-4 and c= -5.

Therefore,

$m + n = \frac{ - ( - 4)}{1} = 4 \: and \: mn = \frac{ - 5}{1} = - 5$

Now,

${m}^{2} + {n}^{2} = {(m + n)}^{2} - 2mn = {4}^{2} -2( - 5)$

$= 16 + 10 = 26$

And,

${m}^{ - 1} + {n}^{ - 1} = \frac{1}{m} + \frac{1}{n} = \frac{m + n}{mn} = \frac{ - 4}{ 5}$

Hope it helps you.