Question

Use the discriminant to describe the roots of each equation 16x^2+8x+1=0

Answer 1

In any quadratic equation: ax² + bx + c = 0,
the discriminant is Δ = b² - 4.a.c

1) If Δ > 0 → we have 2 distinguished roots
2) If Δ = 0 → we have 2 EQUAL roots
3) If Δ < 0 → we have no real roots (we call the results imaginary or complex)

16x² +8x + 1 = 0
Δ = 8² - 4(16)(1) →Δ = 64 - 64 = 0

Since Δ = 0, we have 2 equal roots→ x' = x"

Solve the equation: 

x' = [(-8)+√0]/2(16) = -8/32 = -1/4

x" = [(-8)-√0]/2(16) = -8/32 = -1/4