Question

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

Answer 1

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 of roots (α + β) = 1
• Product of roots (αβ) = 1

TO FIND:

• Quadratic polynomial

SOLUTION:

We know that

Quadratic polynomial = x² - (sum of zeroes)x + product of roots

→ Quadratic polynomial = x² - (1)x + 1

Hence , required quadratic polynomial = x² - x + 1