If \( x^{2}+p x+1 \) is a factor of \( a x^{3}+b x+c \), then
(a) \... VIDEO
If \( x^{2}+p x+1 \) is a factor of \( a x^{3}+b x+c \), then
(a) \( a x+c \) is also a factor of \( a x^{3}+b x+c \)
(b) \( a p+c=0 \)
(c) \( a^{2}-c^{2}=a b \)
(d) \( (2 a-b)^{2}=b^{2}+4 c^{2} \)
(W)
📲 PW App Link - https://bit.ly/YTAI_PWAP
🌐 PW Website - https://www.pw.live/
Other Videos By PW Solutions 2023-02-25 Let \( f(x)=a x^{2}+b x+c \). If \( x_{1}, x_{2}, x_{3} \) are thre... 2023-02-25 Let \( E=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & ... 2023-02-25 Let \( f(x)=a x^{2}+b x+c \). If \( x_{1}, x_{2}, x_{3} \) are thre... 2023-02-25 Let \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \)... 2023-02-25 Each question in this section has four choices (a), (b), (c) and (d... 2023-02-25 The least number of imaginary roots of the equation
\[
P(x)=x^{9}-x... 2023-02-25 Let \( A \) be as in problem 7 and \( B=2 A-I \) where \( I \) is t... 2023-02-25 The number of ways of distributing 10 identical objects among 8 per... 2023-02-25 The number of real roots of \( x^{3}-3 x+1=0 \) lying in the interv... 2023-02-25 Let \( f(x)=a x^{2}+b x+c \). If \( x_{1}, x_{2}, x_{3} \) are thre... 2023-02-25 If \( x^{2}+p x+1 \) is a factor of \( a x^{3}+b x+c \), then
(a) \... 2023-02-25 Let \( f(x)=a x^{2}+b x+c \) where \( a, b, c \in \mathbf{R} \). Su... 2023-02-25 If \( \alpha, \beta, \gamma \) are the roots of \( x^{3}-13 x+11=0 ... 2023-02-25 Let \( -1 \leq p \leq 1 \) and \( p(x)=4 x^{3}-3 x-p \)
(a) \( p(x)... 2023-02-25 If \( \alpha, \beta \) are roots of \( p x^{2}+q x+r=0 \), then the... 2023-02-25 Each question in this section has four choices (a), (b), (c) and (d... 2023-02-25 Each question in this section has four choices (a), (b), (c) and (d... 2023-02-25 Each question in this section has four choices (a), (b), (c) and (d... 2023-02-25 Let \( a, b, c, d \) and \( p \) be integers such that \( p \neq 0 ... 2023-02-25 The equation \( \log _{x^{2}+6 x+8}\left(\log _{2 x^{2}+2 x+3}\left... 2023-02-25 Let \( P(x)=a_{0}+a_{1} x+\ldots+a_{n} x^{n}, a_{n} \neq 0 \) be su...