Question

If m and n are zeroes of polynomial x2 + 2x – 1, then find the value of the following equation:​

Answer 1

Step-by-step explanation:

sum of zeroes = m+n = -2/1 = -2

products of zeros = mn = -1/1 = -1

Now,

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

So,

(m-n) = √ (4 +4) = √8 = 2√2

(m+n) = -2

Add given eq.

(m-n) + (m+n) = -2 + 2√2

=> 2m = 2(√2 -1 )

=> m = -1 + √2

A/Q,

${ |m - 1| }^{ {(m - n)}^{2} } = { { | - 2 + \sqrt{2} | }^{(2 \sqrt{2}) } }^{3} \\ = { | - 2 + \sqrt{2} | }^{8}$