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Step-by-step explanation:
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Answer:
px^2 + qx + q = 0.
alpha / beta = A/ B [ratio ]
let roots of polynomial be "alphaA and alpha B "
sum of zeros =
alphaA + alphaB = - q/ p........
alpha [ A+B] = -q/p
a+ b = -q/p alpha .......eqn 1.....
products of zeroes =
alpha A × alpha B = q /p
AB alpha^2 = q / p.
AB = q / p alpha ^2.........eqn 2....
now,
root A / root B + root B / root A + root q / root p
= a+b /root ab + root q / root p.
= -q/ p /1/alpha × root q/root p + root q / root p.
[ via substitute values from eqn 1 ]..
- root q /root p + root q / root p.
[ have opposite signs ]
so = 0...
hence proved....
want to understand??? I ll tell u in school
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