Question

if a and ß are the roots of the quadratic equation 2x² - x - 1=0,find a and ß

Answer 1

Let the roots be p and q,

2x^2 - x -1 = 0
ax^2 + bx + c = 0 is the general formula,

a = 2
b = -1
c = -1

p+q = -b/a = 1/2. (1)
pq = c/a = -1/2. (2)

(p-q)^2 = (p+q)^2 - 4pq
p-q = √ (1/4 + 2). [ From (1) and (2) ]
p-q = 3/2. (3)


From (1) and (3)
p = 1
q = -1/2

Hope this helps... plsss make it the brainliest