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If X3 − 3x2 + 3x − 7 = (X + 1) (Ax2 + Bx + C), Then a + B + C = - Mathematics

MCQ

If x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c), then a + b + c =

Options

  • 4

  • 12

  • -10

  • 3

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Solution

The given equation is

x3 − 3x2 + 3x − 7 = (x + 1) (ax2 + bx + c)

This can be written as

\[x^3 - 3 x^2 + 3x - 7 = \left( x + 1 \right)\left( a x^2 + bx + c \right)\]

\[ \Rightarrow x^3 - 3 x^2 + 3x - 7 = a x^3 + b x^2 + cx + a x^2 + bx + c\]

\[ \Rightarrow x^3 - 3 x^2 + 3x - 7 = a x^3 + \left( a + b \right) x^2 + \left( b + c \right)x + c\]

Comparing the coefficients on both sides of the equation.

We get,

      a=1 ....... (1)

  a+b = -3 ......... (2)

  b+c =3 ......... (3)
       c = -7 .......(4)
Putting the value of a from (1) in (2)

We get,

1+b =-3

b=-3 -1

b=-4

So the value of a, b and c is 1, – 4 and -7 respectively.

Therefore,

a + b + c =1 - 4 - 7 = -10

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Q 15 | Page 26
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