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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Given zeroes of a polynomial are α = 1/2 , β = 3/2 we know that when α and β are the zeroes of a polynomial then the polynomial is K[x² - (α+β)x + αβ] here α+β = 1/2 + 3/2 = (1+3)/2 = 4/2 = 2 αβ = (1/2)(3/2) = 3/4 now substituting these values in the formula K[ x² - (α+β)x + αβ] =K[ x² - (2)x + 3/4] =K[ x² - 2x +3/4] =K[ (4x² - 2x + 3)/4] Let take K = 4 to remove the fraction form of it 4[ (4x² - 2x + 3)/4] = 4x² -2x +3 ∴4x² - 2x + 3 is the quadratic polynomial