Solving 2x² - 5x + 1 = 0 Using the Formula

Algebra 1 · Axiom Academy

EXAMPLE Solving a Quadratic Using the Formula Identify a , b , c and apply the quadratic formula to solve 2x^2 - 5x + 1 = 0 . Solve the quadratic equation 2x^2 - 5x + 1 = 0 by identifying the coefficients a , b , and c , then applying the quadratic formula. Nice work! You solved a quadratic by identifying its coefficients and running them through the quadratic formula. Remember: Standard form first: read a , b , c from ax^2 + bx + c = 0 — and keep the signs ( b = -5 , not 5 ). The discriminant predicts the count: b^2 - 4ac tells you how many real solutions exist before you finish solving. Positive discriminant: two distinct real solutions — here . The formula always works: it solves any quadratic, factorable or not. Check a solution by substituting it back into 2x^2 - 5x + 1 = 0 — both should return zero.

This is the written version of the interactive lesson above. See the full Algebra 1 course.