Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Unit Tests (Algebra) {Chapters Covered - 2, 4}, Exercise 1: UNIT TEST 1

If $p=2-a$, then prove that $a^3+6ap+p^3-8=0$

If $x=3$ and $x=0$ are zeroes of the polynomial $2x^3-8x^2+ax+b$, then find the values of $a$ and $b$.

If $a+b=10$ and $a^2+b^2=58$, then find the value of $a^3+b^3$

If $x=1, y=2$ is a solution of the equation $a^{2}x+ay=3$, then find the value of $a$.

When $3$ times the larger of two numbers is divided by the smaller, then the quotient and remainder are $2$ and $7$, respectively. Form a linear equation in two variables for above and give its two solutions.

What are the possible expressions for the dimensions of a cuboid whose volume is $2k{y}^2+6ky-20k$?

If the polynomials $\left(2x^3+k{x}^2+3x-5\right)$ and $\left(x^3+x^2-2x+2k\right)$ leave the same remainder, when divided by $(x-3)$, then find the value of $k$. Also, find the remainder in first case.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter Roshni paid $₹35$ for a book kept for seven days. Write a linear equation which satisfies this data.