If the expression ax^2 + bx + c is equal to 4, when x = 0, leaves a remainder 4 when divided by x + 1 and leaves a -Maths 9th

If the expression ax^2 + bx + c is equal to 4, when x = 0, leaves a remainder 4 when divided by x + 1 and leaves a -Maths 9th
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Given exp. f(x) = ax2 + bx + c ∴ When x = 0, a.0 + b.0 + c = 4 ⇒ c = 4.  The remainders when f(x) is divided by (x + 1) and (x + 2) respectively are f(–1) and f(–2). ∴ f(–1) = a.(–1)2 + b.(–1) + c = 4  ⇒ a – b + c = 4 ⇒ a – b + 4 = 4 ⇒ a – b = 0                ...(i)  f(–2) = a.(–2)2 + b(–2) + c = 6  ⇒ 4a – 2b + 4 = 6 ⇒ 4a – 2b = 2                 ...(ii)  Solving (i) and (ii) simultaneously we get, a = 1, b = 1.
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