Question

if α and β are the zeros of the quadratic polynomial 2x² - 5x + 7, find a polynomial whose zeros are 2α and 2β

Answer 1

Answer:

• The required polynomial is x² - 5x + 14.

Step-by-step explanation:

We have been given that α and β are the zeros of the quadratic polynomial 2x² - 5x + 7.

Find relationship between Zeros:

• Sum of Zeros = -b/a
• α + β = -(-5)/2
• α + β = 5/2
• Product of Zeros = c/a
• αβ = 7/2

Here, We have to find a Polynomial whose zeros are 2α and 2β.

• Sum of Zeros = 2α + 2β
• Sum of Zeros = 2 ( α + β )
• Sum of Zeros = 2 * 5/2
• Sum of Zeros (α + β) = 5

→ Product of Zeros = 2α * 2β

→ Product of Zeros = 4ab

→ Product of Zeros = 4*7/2

→ Product of Zeros(αβ)= 14

Find a polynomial with the given zeros:

• f(x) = k[x² - ( α + β)x + αβ]
• f(x) = x² - (5)x + 14
• f(x) = x² - 5x + 14

Therefore, the required polynomial is x² - 5x + 14.

Answer 2

Answer:

x^2-5x+14.

$\alpha \: and \: \beta \: are \: zeroes \:$