Question

If m and n are the zeroes of the polynomial x2-4x+3, show that 1/m + 1/n–2mn+ 14/3=0

Answer 1

therefore ....it is proved

Answer 2

Given: m,n are the zeroes of the polynomial x²-4x+3

To find: 1/m+ 1/n - 2mn +14/3 = 0                 .................(i)

Solution:

• If m and n are the zeroes of the polynomial, then m and n should satisfy the equation,
• let x=m,

              m² - 4m +3 = 0

• Now solving this equation, and finding value of m,

              m² - m - 3m + 3 = 0

              m(m-1)  - 3(m-1) = 0

              (m-3)(m-1) = 0

• So, m=3 and m=1

• Similarly the values for n will be n=3 and n=1

• Now we have two conditions,

                1. m=1 and n=3,

•  Putting these values in equation (i), we get,

                 1/1 + 1/3 - 2(1)(3) + 14/3 = 0

                -5+5=0

• Hence this case satisfy

              2. n=1 and m=3

                   1/3 + 1/1 - 2(3)(1) + 14/3 = 0

                -5+5=0

• hence this also satisfy

Answer:

• Since both the case satisfies -5+5=0, hence it is proved.