Math Problem Statement
p(x) = 2x^3 + ax^2 + bx + 4 roots of this equation are x=1/2, n, -n, find a and b
Solution
Given the polynomial with roots , we can use Vieta's formulas to find the values of and .
Step 1: Expand the Polynomial in Terms of Roots
Since the roots of the polynomial are , we can express as:
Simplifying :
So,
Expanding :
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Vieta's Formulas
Formulas
Vieta's formulas for polynomial roots
Expansion of polynomial (x - r1)(x - r2)(x - r3)
Theorems
Vieta's Theorem
Suitable Grade Level
Grades 10-12
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