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 solve the problem step by step.

**(a) Use the factor theorem to show that ( a = -

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Factor Theorem
Roots of Polynomials

Formulas

f(c) = 0 when (x - c) is a factor
Discriminant analysis for cubic equations

Theorems

Factor Theorem

Suitable Grade Level

Grades 10-12

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