Match the following with I- II- III If x2-x-3-x3-1-A-x-1-Bx-C-x2-x-1 thenI A- a 0II B- b 1III C- c -2

The correct option is B b, a, c x^2 x+3/x^3 1=A(x^2+x+1)+(Bx+C)(x 1)/(x 1)(x^2+x+1) equating the co efficients we get A+B=1 A B+C= 1 A C=3 Sol ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

Match the fol...

Question

Match the following with I, II, III
If $\frac{x^{2} - x + 3}{x^{3} - 1} = \frac{A}{(x - 1)} + \frac{B x + C}{(x^{2} + x + 1)}$ then

I) $A =$ a) 0
II) $B =$ b) 1
III) $C =$ c) -2

a, b, c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

b, a, c

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

b, c, a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a, c,b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B b, a, c
$\frac{x^{2} - x + 3}{x^{3} - 1} = \frac{A (x^{2} + x + 1) + (B x + C) (x - 1)}{(x - 1) (x^{2} + x + 1)}$
equating the co-efficients we get
$A + B = 1$
$A - B + C = - 1$
$A - C = 3$
Solving we get $A = 1; B = 0; C = - 2$
So, $A \equiv b; B \equiv a; C \equiv c$
b,a,c

Suggest Corrections

Similar questions

\frac{x^{2} - x - 3}{x^{3} - 1} = \frac{A}{x - 1} + \frac{B x + C}{x^{2} + x + 1} \Rightarrow 2 A + B + C =

Q. If

\frac{x^{2} + 3}{x^{4} (x + 3)} = \frac{A}{(x + 3)} + \frac{B}{x} + \frac{C}{x^{2}} + \frac{D}{x^{3}} + \frac{E}{x^{4}}

then
Match the following with I, II, III, IV, V

1) A	a) $\frac{4}{9}$
2) C	b) $\frac{4}{27}$
3) B	c) $- \frac{1}{3}$
4) E	d) $- \frac{4}{27}$
5) D	e) 1

Match the following:
$\begin{matrix} (i) Amphibians and most reptiles & A. 2-chambered heart (ii) Birds and mammals & B. 3-chambered heart (iii) Fish & C.4-chambered heart \end{matrix}$

Q. If

\frac{(x - 1)^{2}}{x^{3} + x} = \frac{A}{x} + \frac{B x + C}{x^{2} + 1}

, then

A = . . ., B = . . ., C = . . .

Q. Prove that

\frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)} = 1

Join BYJU'S Learning Program

Match the following with I, II, III If x2−x+3x3−1=A(x−1)+Bx+C(x2+x+1) thenI) A= a) 0II) B= b) 1III) C= c) -2

The correct option is B b, a, cx2−x+3x3−1=A(x2+x+1)+(Bx+C)(x−1)(x−1)(x2+x+1)equating the co-efficients we getA+B=1A−B+C=−1A−C=3Solving we get A=1;B=0;C=−2So, A≡b;B≡a;C≡cb,a,c

Match the following with I, II, III
If $\frac{x^{2} - x + 3}{x^{3} - 1} = \frac{A}{(x - 1)} + \frac{B x + C}{(x^{2} + x + 1)}$ then

I) $A =$ a) 0
II) $B =$ b) 1
III) $C =$ c) -2

The correct option is B b, a, c
$\frac{x^{2} - x + 3}{x^{3} - 1} = \frac{A (x^{2} + x + 1) + (B x + C) (x - 1)}{(x - 1) (x^{2} + x + 1)}$
equating the co-efficients we get
$A + B = 1$
$A - B + C = - 1$
$A - C = 3$
Solving we get $A = 1; B = 0; C = - 2$
So, $A \equiv b; B \equiv a; C \equiv c$
b,a,c