Question

find the quadratic polynomial whose 1 of the zeroes is root 3 by 4 and product of the zeroes is -1 by 2​

Answer 1

Answer:

P(x) = 4√3x² + 5 - 2√3

Step-by-step explanation:

One zero of P(x) = √3 / 4

Let the other zero be a

Product of zeroes = -1 / 2

⇒ √3x / 4 = -1 / 2

⇒ √3x / 2 = -1

⇒ x = -2 / √3

P(x) = k ( x² - (α + β) + αβ)

= k ( x² - ( √3/4 - 2/√3 ) - 1/2 )

= k ( x² - ( -5 / 4√3 ) - 1/2 )

= k ( x² + 5 / 4√3 - 1/2 )

= If k = 4√3 then

P(x) = 4√3x² + 5 - 2√3