Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1​

Answer 1

Answer:

• x² - 4x + 1 = 0

Step-by-step explanation:

Given that,

Sum of zeroes = α+β = 4

Product of zeroes = αβ = 1

∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:-

↪ x² - (α+β)x+αβ = 0

↪ x² - 4x+1 = 0

Thus, x²-4x+1 is the quadratic polynomial.

Answer 2

Answer :-

• The quadratic polynomial is x² - 4x + 1

Given :-

• Sum and product of the zeroes of a quadratic polynomial as 4 and 1 respectively.

To Find :-

• The quadratic polynomial.

Solution :-

Here,

• sum of zeroes (α + β) = 4
• product of zeroes (α × β) = 1

As we know that

Formula for finding the quadratic polynomial is

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

According to question :-

x² - (α + β)x + (α × β)

→ x² - (4)x + 1

→ x² - 4x + 1

Hence, the quadratic polynomial is x² - 4x + 1.