If frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3) | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $\frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3)} = \frac{3}{x - 1} + \frac{2}{x + 2} - \frac{5}{2x + 3}$.Multiplying both sides by the denomina

Vedclass · Accepted Answer

$a = 5$

Vedclass · Answer

(A) Given $\frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3)} = \frac{3}{x - 1} + \frac{2}{x + 2} - \frac{5}{2x + 3}$.Multiplying both sides by the denominator $(x - 1)(x + 2)(2x + 3)$,we get:$ax^2 + bx + c = 3(x + 2)(2x + 3) + 2(x - 1)(2x + 3) - 5(x - 1)(x + 2)$.Expanding the terms:$3(2x^2 + 7x + 6) + 2(2x^2 + x - 3) - 5(x^2 + x - 2)$$= (6x^2 + 21x + 18) + (4x^2 + 2x - 6) - (5x^2 + 5x - 10)$$= (6 + 4 - 5)x^2 + (21 + 2 - 5)x + (18 - 6 + 10)$$= 5x^2 + 18x + 22$.Comparing coefficients,we get $a = 5$,$b = 18$,and $c = 22$.Thus,$a = 5$ is correct.

If $\frac{ax^2 + bx + c}{(x - 1)(x + 2)(2x + 3)} = \frac{3}{x - 1} + \frac{2}{x + 2} - \frac{5}{2x + 3}$,then:

Similar Questions

If $\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$ then $p\left(\frac{3}{2}\right)+C=$

If $\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1} + \frac{Bx+C}{2x^2+3}$,then $A-B+C=$

Resolve $\frac{x + 1}{(x - 1)(x - 2)(x - 3)}$ into partial fractions.

If $\frac{x^2+x+1}{x^2+2x+1}=A+\frac{B}{x+1}+\frac{C}{(x+1)^2}$,then $A-B$ is equal to

If $\frac{2x^2-3x+5}{(x-7)^3}=\frac{A}{x-7}+\frac{B}{(x-7)^2}+\frac{C}{(x-7)^3}$, then $2A-3B+C=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module