Question

Find the quadratic polynomial whose zeroes are -2 root/3 and root3/4

Answer 1

Here is Your Answer.

Given Zeroes :
3 + √5/5 and 3 - √5/5

Sum of Zoroes = 3 + √5/5 + 3 - √5/5
= 6

Product Of Zeroes = (3 + √5/5)(3 - √5/5)
= 3² - (√5/5)²
= 9 - 5/25
= 225/25 - 5/25 = 220/25
= 44/5

Now, Using Basic Equation of Quadratic Equation,
p (x) = kx² - (Sum of Zeroes)x + (Product Of Zeroes)
p (x) = x² - 6x + 44/5

Now, Multiply Whole Equation by 5....
p(x) = 5x² - 30x + 44

Hope It Helps.