Question

If m and n are the zeroes of the quadratic polynomial
f(x)= x²+ 7x +7, then 1/m + 1/n = ?​

Answer 1

Answer:

Given :-

If m and n are the zeroes of the polynomial x² + 7x + 7

To Find :-

Quadratic polynomial

Solution :-

Here

α + β = m + n

m + n = -b/a

Where

b = 7

a = 1

m + n = -(7)/1

m + n = -7

Product of zeroes = αβ = mn

mn = c/a

c = 7

a = 1

mn = 7/1

mn = 7

Now

New sum of the zeroes = 2m + 2n = 2(m + n) = 2(-7) = -14

New product of zeroes = 2m × 2n = 4(m × n) = 4(7) = 28

Now

We know that

Polynomial = x² - (α + β)x + αβ

Polynomial = x² - (-14)x + 28

Polynomial = x² + 14x + 28

Step-by-step explanation: