Question

If alpha and beta are zeroes of 4x^2-6x+1 what is alpha^2-beta^2?​

Answer 1

Answer:

         α² - β² = ±3√5 / 4

Step-by-step explanation:

The roots of 4x² - 6x + 1 are

  ( 6 ± √(6² - 4×4×1) ) / (2×4)

= ( 6 ± √20 ) / 8

= ( 3 ± √5 ) / 4.

So...

• α = (3 + √5)/4   and   β = (3 - √5)/4       (or the other way around).

From here,

• α + β = 3/2
• α - β = √5/2             (or -√5/2, if α and β are swapped)
• α² - β² = (α+β)(α-β) = 3√5 / 4     (or minus that if α and β swapped)