Question

Form the quadratic equation from the roots given below. 

i. 0 and 4 

ii. 3 and -10

iii. \(\frac{1}{2}, \frac{1}{2}\)

iv. 2 – √5, 2 + √5

Answer 1

i. Let a = 0 and β = 4 

∴ α + β = 0 + 4 = 4 

and α × β = 0 × 4 = 0

∴ The required quadratic equation is

x² – (α + β) x + αβ = 0

∴ x² – 4x + 0 = 0

∴ x² – 4x = 0

ii. Let α = 3 and β = -10 

∴ α + β = 3 – 10 = -7 

and α × β = 3 × -10 = -30

∴ The required quadratic equation is

x² – (α + β)x + αβ = 0 

∴ x² – (-7) x + (-30) = 0

\(\therefore\) The required quadratic equation is

∴ The required quadratic equation is

x² – (α + β) x + αβ = 0 

∴ x² – 4x – 1 = 0