Question

find the quadratic polynomial the sum and the product of whose zeros are 4 and 1 respectively

Answer 1

quadratic polynomial
=
${x}^{2} - (sum of roots)x + product of roots \\ = {x}^{2} - (4 + 1)x + (4 \times 1) \\ = {x}^{2} - 5x + 4$

Answer 2

AnswEr :-

• The quadratic polynomial is x² - 5x + 4.

Given :-

• Zeroes of a quadratic polynomial are 4 and 1 respectively.

To Find :-

• The quadratic polynomial.

SoluTion :-

We've to find the quadratic polynomial.

Sum of zeroes :-

4 + 1 (α + β)

→ 5

Product of zeroes :-

4 × 1 (α × β)

→ 4

Formula of quadratic polynomial is :-

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

→ x² - (α + β)x + (α × β)

→ x² - (5)x + (4)

→ x² - 5x + 4

Hence, the quadratic polynomial is x² - 5x + 4.

_____________________

________________________________