if x^2 - ax + b and x^2 - px + q have a root in common and the second equation has equal roots then b + q =
Feliciano:
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x² - a x + b has roots: r, s
=> r + s = a and r s = b
x² - p x + q has roots: r, r
=> p = 2 r and q = r²
b = r s = r * (a - r) = r a - r² = r a - q
=> b + q = r a = a p /2 or a √q
=> r + s = a and r s = b
x² - p x + q has roots: r, r
=> p = 2 r and q = r²
b = r s = r * (a - r) = r a - r² = r a - q
=> b + q = r a = a p /2 or a √q
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