Question

# If 1(x âˆ’ 1)(x + 2)(2x + 3) can be expressed as Ax âˆ’ 1 + Bx + 2 + C2x + 3 then what will be the respective values of A, B and C?

A

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

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

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B The approach to solve these kind of questions should be by cross checking. Let's take LCM of Ax − 1 + Bx + 2 + C2x + 3 and rewrite this- A(x + 2)(2x + 3) + B(x − 1)(2x + 3) + C(x − 1)(x + 2)(x − 1)(x + 2)(2x + 3) or A(2x2 + 3x + 2x + 6) + B(2x2 + 3x − 2x − 3) + C(x2 + 2x − x − 2(x − 1)(x + 2)(2x + 3) or x2(2A + 2B + C) + x(5A + B + C) + 6A − 3B − 2C(x − 1)(x + 2)(2x + 3) Now we'll compare the expression we got with the given expression. That is, comparing the numerator of the above expression with numerator of 1(x − 1)(x + 2)(2x + 3) So, 2A + 2B + C = 0 (coefficient of x2 = 0) 5A + B + C = 0 (coefficient of x = 0) 6A - 3B - 2C = 1 We have three equations and three variables. On solving these equations we get A = 115, B = 13, C = 4−5 We can also put the values given in the options and check which option satisfies these 3 equations.

Suggest Corrections
0
Related Videos
Integration by Partial Fractions
MATHEMATICS
Watch in App