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AP EAMCET202316 May 2023Morning ShiftMathematicsQuadratic EquationActual

In x^4-6 x^3+9 x^2+5 x-20 x^2-x-2 =f(x)+ a x+p + b x+q then 2(a+b)=

Options

  1. Af (7)
  2. Bf (6)
  3. Cf (5)
  4. Df (4)

Correct answer

D. f (4)

Step-by-step solution

Given : x^4-6 x^3+9 x^2+5 x-20 x^2-x-2 =f(x)+ a (x+p) + b (x-q) ...(i) aligned & x^4-6 x^3+9 x^2+5 x-20 x^2-x-2 & = (x^2-5 x+6 )+ x-8 x^2-x-2 & = (x^2-5 x+6 )+ x-8 (x+1)(x-2) & x^4-6 x^3+9 x^2+5 x-20 x^2-x-2 aligned = (x^2-5 x+6 )+ 3 x+1 - 2 x-2 ...(ii) Comparing eqns. (i) and (ii), we get aligned & f(x)=x^2-5 x+6, a=3, b=-2 & p=1, q=2 & 2(a+b)=2(3-2)=2 1=2 & Now, f(7)=49-35+6=20 & f(6)=36-30+6=12 & f(5)=25-25+6=6 & f(4)=16-20+6=2 & 2(a+b)=f(4) . aligned

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