If the roots of the given equation (cos p - 1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $(\cos p - 1){x^2} + (\cos p)x + \sin p = 0$. Since the roots are real,the discriminant $D \ge 0$. $D = b^2 - 4ac = (\cos p)^2 - 4

Vedclass · Accepted Answer

$p \in (0,\pi )$

Vedclass · Answer

(C) Given equation: $(\cos p - 1){x^2} + (\cos p)x + \sin p = 0$. Since the roots are real,the discriminant $D \ge 0$. $D = b^2 - 4ac = (\cos p)^2 - 4(\cos p - 1)(\sin p) \ge 0$. $\cos^2 p - 4\sin p \cos p + 4\sin p \ge 0$. For the quadratic equation to be valid,the coefficient of $x^2$ must not be zero,so $\cos p - 1 
eq 0$,which implies $p 
eq 2n\pi$. Analyzing the inequality,for $p \in (0, \pi)$,$\sin p > 0$ and $(1 - \sin p) \ge 0$. Thus,the condition $D \ge 0$ is satisfied for $p \in (0, \pi)$.

If the roots of the given equation $(\cos p - 1){x^2} + (\cos p)x + \sin p = 0$ are real,then

Similar Questions

$A = \{x_1, x_2, x_3, x_4\}$; $B = \{y_1, y_2, y_3, y_4\}$. $A$ function $f: A \to B$ is defined. The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

Isogamous condition with non-flagellated gametes is found in:

Total number of secondary amines (excluding stereoisomers) possible with the molecular formula $C_5H_{13}N$ is

If the number average molecular weight and weight average molecular weight of a polymer are $40000$ and $60000$ respectively,the polydispersity index of the polymer will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module