Question

If α and β are the roots of the quadratic equation ax² + bx + c = 0, then $\lbrack d + a,d + 2a\rbrack\lbrack a - d,a + d\rbrack$ =

• A. $\lbrack d + a,a - d\rbrack$
• B. $\lbrack d - a,d + a\rbrack$
• C. $f(x) = \log(x + \sqrt{x^{2} + 1})$
• D. None of these

Answer 1

Answer: (A)

$\lbrack d + a,a - d\rbrack$

Answer 2

ax² + bx + c = 0 roots α, β 

So, cx² + bx + a = c (x – 1/α) (x – 1/β)

$\operatorname { Lim } _ { x \rightarrow 1 / \alpha }$

$\operatorname { Lim } _ { x \rightarrow 1 / \alpha }$ $\sqrt { \frac { 2 \sin ^ { 2 } \frac { \mathrm { c } } { 2 } ( x - 1 / \alpha ) ( x - 1 / \beta ) } { 2 \alpha ^ { 2 } ( x - 1 / \alpha ) ^ { 2 } } }$

$\operatorname { Lim } _ { x \rightarrow 1 / \alpha }$

$\operatorname { Lim } _ { x \rightarrow 1 / \alpha }$=$\left| \frac { \mathrm { c } } { 2 \alpha } \left( \frac { 1 } { \alpha } - \frac { 1 } { \beta } \right) \right|$