If ax^2 + bx + c = 0 has equal roots, then c = A. –b/2a B. b/2a C. (-b^2)/4a D. b^2/4a

Question

If ax² + bx + c = 0 has equal roots, then c =

A. –b/2a

B. \(\frac{b}{2a}\)

C. \(\frac{-b^2}{4a}\)

D. \(\frac{b^2}{4a}\)

Answer 1

Let the roots of given equation be m and n 

According to the question M = n 

Sum of roots = m + n = – b / a

\(2m=-b/a\)

\(\Rightarrow m=-b/2a\)

Product of roots = m × n = \(c/a\)

m2 = \(c/a\)

\((-b/2a)^2=c/a\)

\(b^2/4a^2=c/a\)

\(b^2/4a^2=c\)

Therefore c = \(\frac{b^2}{4a}\)