Question

form the quadratic equation if the roots of quadratic equation are 1/2 & -1/2​

Answer 1

Answer:

• 4x² - 4x - 1 = 0

Step-by-step explanation:

Given that,

• Roots of quadratic equation is 1/2 & -1/2.

✒ Sum of roots,

⟹ α + β = (1/2) + (-1/2)

⟹ α + β = 1/2 - 1/2

⟹ α + β = 1

✒ Product of roots,

⟹ αβ = 1/2 × -1/2

⟹ αβ = -1/4

As we know that,

✒ Quadratic equation = x² - (α + β)x + αβ = 0

⟹ Quadratic equation = x² - (1)x + (-1/4) = 0

⟹ Quadratic equation = x² - x - 1/4 = 0

[ Multiply by 4 on each sides ]

⟹ Quadratic equation = 4x² - 4x - 1 = 0.