Question

find the quadratic polynomial if sum of the zeroes is 1 and product of its zeroes is 1​

Answer 1

Answer:

Therefore, the required polynomial is x² - x + 1.

Step-by-step explanation:

GIVEN:

Sum of zeroes of quadratic polynomial = 1

Product of zeroes of quadratic polynomial = 1

TO FIND:

The quadratic polynomial

SOLUTION:

We know that, the standard form of quadratic polynomial is,

x² - (sum of zeroes)x + product of zeroes

Sum of zeroes = 1

Product of zeroes = 1

==> x² - (1)x + 1

==> x² - 1x + 1

Therefore, the required polynomial is x² - x + 1.

Answer 2

Given : Sum fo zeroes = (α+β)=0Product of the zeroes = αβ=−1Required quadratic polynomial isx²−(α+β)x+αβ=x²−(0)x−1=x²−1Now, find the zeroes of the above polynomial.Let f(x)=x²−1= x²−1²=(x−1)(x+1)Substitute f(x)=0(x−1)=0 or (x+1)=0⇒x=1 or x=−1