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If lampa and beeta are the zeroes of a quadratic polynomial such that lampa +beeta =24 and lamps -beeta =8 find the quadratic polynomial having lamps and beeta as its zeroes verify the relationship between zeroes and coefficient of polynomial |
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Answer» polynomial EQ. is x² - 24x + 128 Step-by-step explanation: α + β = 24 ------------(1) α - β = 8 -------------(2) by using elimination METHOD on adding eq. 1 and 2 α + β = 24 α - β = 8 ............................ 2α = 32 α = 32/2 α = 16 PUT α in eq. 1 α + β = 24 16 + β = 24 β = 24 - 16 β = 8 now, polynomial eq is x² - (α + β)x + αβ = 0 x² - (16+ 8)x + 16×8 = 0 x² - 24x +128 = 0 we KNOW that , zeroes of polynomial is α and β verification of zeroes sum of zeroes = -b/a 16 + 8 = -(-24)/1 24 = 24 PRODUCT of zeroes = c/a 16 × 8 = 128/1 128 = 128
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