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. If the root of the equation (a - b)x² + (6 - ce it ((-a) =are equalshow that ca andb are in AP. |
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Answer» Step-by-step explanation:we know that when roots of quadratic equations are equal then =) DISCRIMINANT (D) = 0 Given equation is , =) (b-c)x2 + (c-a)x +(a-b) = 0 D = (c-a)^2 - 4(b-c)(a-b) = 0 =)(c^2 + a^2 -2ac) - 4(ab -b^2 -ac + bc )=0 =) c^2 + a^2 -2ac - 4AB + 4b^2 +4ac -4bc =0 =) a^2 + 4b^2 +c^2 -4ab - 4bc + 2ac =0 =) ( a -2B + c)^2 = 0 =) a -2b + c = 0 =) a +c = 2b ---------*(1) we can write this expression as =) (b - a )= (c -b ) so this is required condition for a , b ,c therefore a, b ,c are in A.P proved ___________________________________________________ Hope it will help u ^_^ |
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