Nilai 𝑞 yang memenuhi persamaan (𝑥
2 + 𝑝𝑥 + 𝑞)(𝑥
2 − 3𝑥 + 1) = 𝑥
2 − 6𝑥
3 + 15𝑥
2 −
18𝑥 + 5 adalah ….

Diberikan persamaan berikut:

\[
(𝑥^2 + 𝑝𝑥 + 𝑞)(𝑥^2 − 3𝑥 + 1) = 𝑥^2 − 6𝑥^3 + 15𝑥^2 − 18𝑥 + 5
\]

Mari kita mulai dengan mengembangkan bentuk kiri persamaan.

Ekspansi dari \((𝑥^2 + 𝑝𝑥 + 𝑞)(𝑥^2 − 3𝑥 + 1)\) adalah:

\[
(𝑥^2 + 𝑝𝑥 + 𝑞)(𝑥^2 − 3𝑥 + 1) = 𝑥^2(𝑥^2 − 3𝑥 + 1) + 𝑝𝑥(𝑥^2 − 3𝑥 + 1) + 𝑞(𝑥^2 − 3𝑥 + 1)
\]

Sekarang, mari kita hitung ekspansi tersebut:

1. \(𝑥^2 \times (𝑥^2 − 3𝑥 + 1) = 𝑥^4 − 3𝑥^3 + 𝑥^2\

Explore the solution to the polynomial equation (𝑥^2 + 𝑝𝑥 + 𝑞)(𝑥^2 − 3𝑥 + 1) = 𝑥^2 − 6𝑥^3 + 15𝑥^2 − 18𝑥 + 5 with step-by-step detailed expansion and algebraic manipulation. This problem involves quadratic equations, polynomial expansions, and algebraic expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation