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If p and q are roots of 2x²+x-5=0

p+q = -b/a = -1/2

pq = c/a = -5/2

(p+q)² = (-1/2)²

⇒ p² + q² + 2pq = 1/4

⇒ p² + q² + 2×(-5/2) = 1/4

⇒ p² + q² - 5 = 1/4

⇒ p² + q² = 5+1/4

⇒ p² + q² = 21/4

(p-q)² = p² + q² - 2pq = 21/4 - 2×(-5/2) = 21/4 + 5 = 41/4

⇒ p-q = √(41/4)

⇒ p-q = +√(41)/2 or -√(41)/2

p² - q² = (p+q)(p-q) = -1/2 × √(41) / 2 = -√(41) /4 and

p² - q² = (p+q)(p-q) = -1/2 × -√(41) / 2 = √(41) /4

So the product of roots is

p+q = -b/a = -1/2

pq = c/a = -5/2

(p+q)² = (-1/2)²

⇒ p² + q² + 2pq = 1/4

⇒ p² + q² + 2×(-5/2) = 1/4

⇒ p² + q² - 5 = 1/4

⇒ p² + q² = 5+1/4

⇒ p² + q² = 21/4

(p-q)² = p² + q² - 2pq = 21/4 - 2×(-5/2) = 21/4 + 5 = 41/4

⇒ p-q = √(41/4)

⇒ p-q = +√(41)/2 or -√(41)/2

p² - q² = (p+q)(p-q) = -1/2 × √(41) / 2 = -√(41) /4 and

p² - q² = (p+q)(p-q) = -1/2 × -√(41) / 2 = √(41) /4

So the product of roots is