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Show that all the following are equivalent: (а) т? — 5х +6 — 0. (Ъ) (т — 2)(т — 3) — 0. (c) x – 2 = 0 or x – 3 = 0. (d) x = 2 or x = 3. %3D

Show that all the following are equivalent: (а) т? — 5х +6 — 0. (Ъ) (т — 2)(т — 3) — 0. (c) x – 2 = 0 or x – 3 = 0. (d) x = 2 or x = 3. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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## Problem 7.17 ### Objective Show that all the following are equivalent: ### Equations (a) \( x^2 - 5x + 6 = 0 \) (b) \( (x - 2)(x - 3) = 0 \) (c) \( x - 2 = 0 \) or \( x - 3 = 0 \) (d) \( x = 2 \) or \( x = 3 \) ### Explanation - **Equation (a)** is a quadratic equation in standard form, which needs to be solved to find the values of \( x \). - **Equation (b)** expresses the quadratic equation in factored form, setting the product of two linear factors to zero. - **Equation (c)** separates the factored equation into individual equations showing the principle of zero-product property. - **Equation (d)** provides the solutions or roots of the quadratic equation, showing the values of \( x \) that satisfy the equation.
Transcribed Image Text:## Problem 7.17 ### Objective Show that all the following are equivalent: ### Equations (a) \( x^2 - 5x + 6 = 0 \) (b) \( (x - 2)(x - 3) = 0 \) (c) \( x - 2 = 0 \) or \( x - 3 = 0 \) (d) \( x = 2 \) or \( x = 3 \) ### Explanation - **Equation (a)** is a quadratic equation in standard form, which needs to be solved to find the values of \( x \). - **Equation (b)** expresses the quadratic equation in factored form, setting the product of two linear factors to zero. - **Equation (c)** separates the factored equation into individual equations showing the principle of zero-product property. - **Equation (d)** provides the solutions or roots of the quadratic equation, showing the values of \( x \) that satisfy the equation.
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