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If a, ß are the roots of the equation ax 2 + bx + c = 0, then find the value of 1/a^2 + 1/ß^2

If a, ß are the roots of the equation ax 2 + bx + c = 0, then find the value of 1/a^2 + 1/ß^2

Grade:upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
The given equation is ax2 + bx + c = 0.
Let the roots of the equation be ∝ and ß.
Then we have, sum of roots = ∝ + ß = -b/a
Product of roots = ∝.ß.= c/a
We are required to find 1/∝2 + 1/ß2.
Hence 1/∝2 + 1/ß2 = ( ß2 + ∝2 )/∝2ß2
= [(∝ + ß)2 – 2∝.ß.] /∝2ß2
= [(-b/a)2 – 2c/a] / (c2/a2)
= [b2/a2 – 2c/a] / (c2/a2)
= [b2 – 2ca] / c2
Hence, this is the required answer.
Thanks & Regards
Latika Leekha
askIITians Faculty

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