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If one zero of the polynomial ax' +bxtc is double the other prove that2 b^{2}=9 a c. |
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Answer» Letα,β are the two zeros of the polynomial ax²+bx+cThen,α+β=-b/a andαβ=c/aBy the given condition,β=2α∴,α+2α=-b/aor, 3α=-b/aor,α=-b/3a -------(1) andα.2α=c/aor, 2α²=c/aor,α²=c/2aor, (-b/3a)²=c/2a [using (1)]or, b²/9a²=c/2aor, b²/9a=c/2or, 2b²=9ac (Proved) |
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