(x - a)(x - b) (x - c)(x - d) = A x - c - B (x - d) + C, then C = - Vidyadip

MCQ

${{(x - a)(x - b)} \over {(x - c)(x - d)}} = {A \over {x - c}} - {B \over {(x - d)}} + C$, then $C =$

A
$5$
B
$4$
C
$3$
✓
$1$

✓

Answer

Correct option: D.

$1$

d
(d) $A(x - d) - B(x - c) + C(x - c)\,(x - d) = (x - a)$$(x - b)$

Equating coefficient of ${x^2},\,C = 1$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from basic of algoritham→basic of algoritham — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The coefficient of $x$ in the equation ${x^2} + px + q = 0$was taken as $17$ in place of $13$, its roots were found to be $-2$ and $-15$, The roots of the original equation are

If $\tan \alpha = \frac{m}{{m + 1}}$ and $\tan \beta = \frac{1}{{2m + 1}}$, then $\alpha + \beta = $

All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is

The value of $m$, for which the line $y = mx + \frac{{25\sqrt 3 }}{3}$, is a normal to the conic $\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1$, is

A man running round a race-course notes that the sum of the distance of two flag-posts from him is always $10\ metres$ and the distance between the flag-posts is $8\ metres$. The area of the path he encloses in square metres is

The equation ${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}}$ is only possible when

$r$ and $n$ are positive integers $r>1, n>2$ and coefficient of $(r+2)$ th term and $3 r$ th term in the expansion of $(1+x)^{2 n}$ are equal, then $n$ equals:

In the expansion of ${\left( {\frac{x}{2} - \frac{3}{{{x^2}}}} \right)^{10}}$, the coefficient of ${x^4}$is

The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to

If $1,\omega ,{\omega ^2}$ are three cube roots of unity, then ${(a + b\omega + c{\omega ^2})^3}$ + ${(a + b{\omega ^2} + c\omega )^3}$ is equal to, if $a + b + c = 0$