Without solving the following equation what is the value of m for whic

Question

Without solving the following equation what is the value of m for which the equation  x^2 + 2(m – 1)x + (m + 5) = 0  has real and equal roots?

A. -4 or -4
B. -1 or -2
C. -1 or -1
D. -1 or 1
E. -1 or 4

GMATinsight · Answer

Sum of roots = -b/a = -2(m-1), Since both roots are equal therefore, each root = -2(m-1)/2 = 1-m

Product of roots = c/a = (m+5)

i.e  (1-m)^2 = m+5 
i.e.  m^2+1-2m = m+5 
i.e.  m^2 = 3m+4 
i.e. m = -1 and 4

Answer: Option E

pratiksha1998 · Answer

Hi,

When we say equal roots, we essentially mean that the equation has 1 solution, so we can use  b^2 = 4ac

and then solve for m?

Bunuel · Answer

Yes, the quadratic equation ax^2 + bx + c = 0 has equal roots if its discriminant b^2 - 4ac = 0.

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