Find a quadratic equation whose roots are 1.5 + √2 and 1.5-√2expressing it in the form of ax^2+bx+c+c=0 where a, b and c are integers with step by step explanations

0 = f (x) = (x - r) (x - s) = x² - (r+s) + rs

We have r=1.5+√2, s=1.5 - √2 so r+s = 3 and

rs = (1.5+√2) (1.5 - √2) = 1.5² - (√2) ² = 2.25 - 2 = 0.25

f (x) = x² - 3x + -.25

For integer coefficients we mulitply by 4,

g (x) = 4f (x) = 4x² - 12x - 1

Answer: 4x² - 12x - 1 = 0