Math, asked by mariamahmmed16, 6 months ago

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

Answers

Answered by chaitalibhowmik12345
2

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.

Similar questions