Find quadratic polynomial if sum and product of zeros are root2 and root(-3/2)
Also, find zeroes
A quadratic polynomial has the form
ax^2 + bx + c
For the zeros, ax^2 + bx + c = 0
sum of roots = -b/a, product of roots are c/a
you told me the sum or roots = √2 and their product is √(-3/2)
so the equation must be
x^2 - √2x + √(-3/2) = 0
for the actual roots
x = (√2 ± √(-1.5 - 4(1)(√-1.5) )/2
awfully messy to solve, so I let Wolfram find it to be
x1 = -.497341 + .207832 i
x2 = 1.41752 - .543991 i
www.wolframalpha.com/input?i=solve+x%5E2+-+%E2%88%9A2x+%2B+%E2%88%9A%28-3%2F2%29+%3D+0