🧮 algebra

1. The problem is to solve the quadratic equation $$7x^2 + 2x + 8 = 0$$ using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to find the coordinate of the point that divides the segment between points A and B in the ratio 3:2. 2. **Identify given points:** Point A is at

1. **State the problem:** Divide the polynomial $x^3 + x^2 - x + 2$ by $x + 4$ using long division. 2. **Recall the long division formula:** When dividing $P(x)$ by $D(x)$, we find

1. **Problem statement:** We are given the equation of a stone archway as $$10x^2 + 9y - 90 = 0$$ and need to write an inequality representing the region below the archway. 2. **Re

1. **State the problem:** Simplify the sum of the two polynomials: $$(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$$

1. **State the problem:** Graph the quadratic inequalities: a) $y > -x^2 - 3x - 4$

1. The problem is to find the square root of 100000. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Fully factorise the expression $$36c^2 - d^2$$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule $$a^2 - b^2 = (a - b

1. We are asked to solve the quadratic equation $m^2 = 4(2m + 5)$. 2. First, expand the right side:

1. The problem is to create a question paper exactly like the SEE (Second Year Engineering Examination) format. 2. Typically, SEE question papers include multiple sections with que

1. **State the problem:** Find the remainder when the polynomial $f(x)$ is divided by $d(x)$ using the Remainder Theorem. 2. **Recall the Remainder Theorem:** If a polynomial $f(x)

1. The problem is to create a math question paper for class 10 or SEE according to the model 2082 approved by CDC Nepal. 2. Since the user requests a question paper, I will provide

1. **State the problem:** Find the range of the function $y = 3x + 2$ for the domain values $x = 4$ and $x = -4$. 2. **Formula and explanation:** The function is linear, so the ran

1. **State the problem:** Find the range of the function $$y=\sqrt{5x+4}$$ for the domain values given. 2. **Identify the domain:** The problem gives multiple domain options, but t

1. The problem is to understand and analyze a polynomial function. 2. A polynomial function is generally expressed as $$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where

1. **State the problem:** Solve the inequality $$\frac{(x - 1)(x - 2)}{(x + 1)(x - 4)} > 0$$. 2. **Recall the rule for rational inequalities:** The expression changes sign at zeros

1. Problema: Hallar el valor numérico de la expresión (a + b) - c - a para a=1, b=2, c=3. 2. Fórmula y reglas: Sustituimos los valores dados en la expresión y realizamos las operac

1. Problem: Find the domain and range of $f(x) = |x - 3|$. 2. The function $f(x) = |x - 3|$ is an absolute value function.

1. **State the problem:** Expand the expression $$(5 + x\sqrt{6})^2$$ and express it as a trinomial. 2. **Formula used:** The square of a binomial $$(a + b)^2$$ is given by $$a^2 +

1. **Stating the problem:** Calculate the determinant of the matrix $$\begin{pmatrix} 1 & 1 & -2 & 0 \\ 3 & 6 & -2 & 5 \\ 1 & 0 & 6 & 4 \\ 2 & 3 & 5 & -1 \end{pmatrix}$$

1. **Problem statement:** We start with $a$ cells, and the population doubles every 30 minutes. We want to find the formula for $f(t)$, the number of cells after $t$ hours. 2. **Un