Question

Write a quadratic equation in standard form that has two solutions, 5 and 7

Answer 1

If x₁ and x₂ are solutions of the quadratic equation, then we can write it in quadratic factorization:

a(x - x₁)(x - x₂)

We have x₁ = 5 and x₂ = 7

(x - 5)(x - 7) = (x)(x) + (x)(-7) + (-5)(x) + (-5)(-7) = x² - 7x - 5x + 35 = x² - 12x + 35

Answer: x² - 12x + 35 = 0