If α, β are the roots of the equation x² - 7x + 12 = 0, then α² + β² equals to:

Question: If α, β are the roots of the equation x² - 7x + 12 = 0, then α² + β² equals to:

Solution:
x² - 7x + 12 = 0
⇒ x² - 3x - 4x + 12 = 0
⇒ x(x - 3) - 4(x - 3) = 0
⇒ (x - 3)(x - 4) = 0
∴ x = 3, 4

Hence, α = 3, β = 4
Hence, The value of α² + β² = 3² + 4² = 9 + 16 = 25