Question

If the difference between the roots of ax2 + bx + c = 0 is 1, then which one of the following is correct?

b2 = a(a + 4c)
a2 = b(b + 4c)
a2 = c(a + 4c)
b2 = a(b + 4c)

Answer 1

Answer:

The correct option is A.

Step-by-step explanation:

Let α and β be the roots of the equation.

Sum = α + β = -b/a

Product = αβ = c/a

α - β = 1

(α - β)2 = α2 + β2 - 2αβ

(α - β)2 = (α + β)2 - 4αβ

1 = (-b/a)2 - 4c/a

1 + 4c/a = b2/a2

a2 + 4ac = b2

b2 = a(a + 4c)

Answer 2

Step-by-step explanation:

1. If ax2 + bx + c = 0 has equal roots, then c= ( a) – 2 b a b a (c) (b) 2 –b2 4a (d) b2 4a 2. Values of ... 1, then (a) b2–4c + 1 =0 (b) b2 + 4c=0 (c) b2–4c – 1 = 0 (d) b2–4c = 0 ...