Question

What value of b will cause 16x ^ 2 + bx + 4 = 0 to have one real solution ?

Answer 1

b = 16

Explanation:

16*x + b*x + 4 = 0

Solving for x we get:

x₁,₂ = - b ± √ b² - 4*a*c ] / 2*a (1)

If we take a look to the square root

√ b² - 4*4*16 = √ b² - 256

if we make √ b² - 256 = 0

b² = 256 ⇒ b = 16

Then equation (1) becomes:

x₁,₂ = ( - 16 ± 0 ) / 32

x = - 1/2