For which value of
(m
) will
(m x^2+(m+3)x+3=0
) have equal roots and remain a quadratic equation?

m=3

For an equation
ax^2+bx+c=0
), equal roots require the discriminant
D=b^2-4ac
to be zero. Here,
a=m, b=m+3, c=3
, so
D=(m+3)^2-12m=(m-3)^2
. Thus,
D=0
gives
m=3
. For this value, the coefficient of
x^2
is
a=m=3
, which is non-zero, so the equation remains quadratic. Although
m=0
also makes the discriminant zero, it removes the quadratic term and therefore does not satisfy the condition. Exam tip: After setting
D=0
, always verify that the coefficient of
x^2
is not zero.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.