Question

38
EXEMPL
11. (x + 1)2 - x? = 0 has
(A) four real roots
(C) no real roots
(B) two real roots
(D) one real root.​

Answer 1

Correct Question

(x + 1)² - x² = 0 has:

a) Four Real Roots

b) No Real Roots

c)Two Real Roots

d) One Real Root

Answer

Given Equation,

$\sf{(x + 1){}^{2} - x{}^{2} = 0 } \\ \\ \implies \: \sf{(x{}^{2} + 2x + 1) - x{}^{2} = 0 } \\ \\ \implies \: \sf{ \cancel{x {}^{2} } + 2x + 1 - \cancel{x {}^{2 }= 0 }} \\ \\ \implies \: \sf{2x + 1 = 0} \\ \\ \huge{\implies \: \underline{\boxed{ \sf{x = \frac{ - 1}{2} }}}}$

$\sf{\therefore , \ the \ given \ equation \ as \ one \ only \ root}$

The correct option is (d) Only One Root

ALITER

After expanding and cancelling the like terms of the above equation,we get an expression :

2x + 1 = 0

As we know that,

Number of roots of an equation relates to the power of the X

Thus,the equation would have one root

Answer 2

Question :

Choose the Correct Option :

Q. (x + 1)² - x² = 0 has

(A) four real roots

(C) no real roots

(B) two real roots

(D) one real root.

AnswEr :

➟ (x + 1)² - x² = 0

➟ (x)² + (1)² + (2 × x × 1) - x² = 0

• (a + b)² = a² + b² + 2ab

➟ x² + 1 + 2x - x² = 0

➟ 1 + 2x = 0

➟ 2x = - 1

➟ x = -1/2

• This Equation has (D) only one root.

჻ (x + 1)² - x² = 0 has only one real root i.e. -1/2.