Mathguru

isi, cmi practice problem: Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1$. What is the remainder when $g(x^{12})$ is divided by the polynomial $g(x)$ ? (a) 6 (b) $5 - x$ (c) $4 - x + x^2$ (d) $3 - x + x^2 - x^3$

isi, cmi practice problem: If $P(x)$ is a polynomial satisfying $P(x^2) = x^2 P(x)$ and $P(0) = -2, P'\left(\frac{3}{2}\right) = 0, P(1) = 0$. Find the maximum value of $P(x)$ is...

isi, cmi practice problem: $y = ax^2 + 2bx + c \ (a, b, c \in R, abc \neq 0)$ never meets x-axis then $a, b, c$ can be in (a) A.P. (b) G.P. (c) H.P. (d) None of these

isi, cmi practice problem: If ‘$a$’ and ‘$b$’ are distinct positive integers and the quadratic equations $(a - 1)x^2 - (a^2 + 2)x + (a^2 + 2a) = 0$ and $(b - 1)x^2 - (b^2 + 2)x + (b^2 + 2b) = 0$ have a common root...