Math Problem Statement

f(x) = 4x^3 - 8x^2 + 5x + a, where a is a constant. Given that (2x - 3) is a factor of f(x), (a) use the factor theorem to show that a = -3. (b) Hence show that the equation f(x) = 0 has only one real root.

Solution

Let’s analyze and solve the given problem step by step:

Part (a): Using the factor theorem to find aa

The polynomial is given as: [ f(x)

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Math Problem Analysis

Mathematical Concepts

Polynomials
Factor Theorem
Roots of Equations

Formulas

Factor Theorem: If (x - k) is a factor of f(x), then f(k) = 0

Theorems

Factor Theorem
Nature of Roots for Polynomials

Suitable Grade Level

Grades 10-12

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