Build the quadratic equation whose solution set is {2, 1/4}. Give the equation in integer-coefficient standard form.

Introduction / Context: Constructing a quadratic from given roots is foundational. When roots are fractional, it is good practice to clear denominators to present an equation with integer coefficients.

Given Data / Assumptions:

• Roots: 2 and 1/4.
• We want a standard form with integer coefficients.

Concept / Approach: Use x^2 − (sum)x + (product) = 0. Compute sum and product carefully with the fraction, then multiply by the least common multiple of denominators to clear fractions.

Step-by-Step Solution:

Verification / Alternative check: Factor check: (4x − 1)(x − 2) = 4x^2 − 8x − x + 2 = 4x^2 − 9x + 2, so roots are 1/4 and 2.

Why Other Options Are Wrong: They represent incorrect arithmetic (wrong sum/product) or not both required roots.

Common Pitfalls: Forgetting to clear denominators or mixing signs in the sum term.

Final Answer: 4x^2 − 9x + 2 = 0