The number of roots of the equation x-2x-5-x-3x-6-x-2-x-4 is

The correct option is C 1 (x+2)(x 5)/(x 3)(x+6)=x 2/x+4 ⇒ (x^2 3x 10)(x+4)=(x^2+3x 18)(x 2) ⇒ x^2 22x 40=x^2 24x+36 ⇒ 2x=76 ⇒ x = 38 Hence, the equation has o ...

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Standard XII

Mathematics

Higher Order Equations

The number of...

Question

The number of roots of the equation $\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4}$ is

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Solution

The correct option is B
1

$\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4} \Rightarrow (x^{2} - 3 x - 10) (x + 4) = (x^{2} + 3 x - 18) (x - 2) \Rightarrow x^{2} - 22 x - 40 = x^{2} - 24 x + 36 \Rightarrow 2 x = 76 \Rightarrow x = 38 H e n c e, t h e e q u a t i o n h a s o n l y 1 r o o t .$

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Similar questions

Q. The number of roots of the equation

\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4}

is
(a) 0
(b) 1
(c) 2
(d) 3

Q. Assertion :The number of minimum possible complex roots of the equation

x^{6} - 3 x^{5} + 4 x^{3} + 3 x^{2} + 4 = 0

2

Reason: The equation

x^{6} - 3 x^{5} + 4 x^{3} + 3 x^{2} + 4 = 0

has maximum four real roots.

Q. The equation

\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4}

has

Q. The maximum possible number of real roots of equation

x^{5} - 6 x^{2} - 4 x + 5 = 0

Q. Solve the following equation that has equal roots:

x^{6} - 2 x^{5} - 4 x^{4} + 12 x^{3} - 3 x^{2} - 18 x + 18 = 0

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The number of roots of the equation (x+2)(x−5)(x−3)(x+6)=x−2x+4 is

The correct option is B 1 (x+2)(x−5)(x−3)(x+6)=x−2x+4⇒(x2−3x−10)(x+4)=(x2+3x−18)(x−2)⇒x2−22x−40=x2−24x+36⇒2x=76⇒x=38Hence, the equation has only 1 root.

The number of roots of the equation $\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4}$ is