Answer:
See below.
Step-by-step explanation:
Given :-
x² + bx + c = 0 if x₁ + x₂ = -b and x₁x₂ = c
Solving :-
a) x₁ = 1/2 and x₂ = -3/4
=> x² + -(1/2 + -3/4)x + 1/2(-3/4)
=> x² + -(-1/4)x + (-3/8)
=> x² + 1/4x - 3/8
=> 8x² + 2x - 3 = 0
b) x₁ = 1 + √5 and x₂ = 1 - √5
=> x² + -(1 + √5 + 1 - √5)x + (1 + √5)(1 - √5)
=> x² - 2x + 1 - 5
=> x² - 2x - 4 = 0
