Math CentralQuandaries & Queries


Question from Najah, a student:

(E): (m2_1)x2 _ (m+3)x+4_m2=0
A) for what values of m is the equation (E) quadratic?
B) for what value of m is the real number -1 a root of (E)

Hi Najah,

I am going to assume your equation is

\[\left( m^2 - 1\right) x^2 - (m + 3) x + 4 - m^2 = 0.\]

A quadratic equation in the variable $x$ is an equation of the form $a x^2 + b x + c = 0$ where $a, b$ and $c$ are constants and $a \neq 0.$ Thus your equation is a quadratic as long as $m^2 - 1 \neq 0.$

For B part, if $-1$ is a root then substituting $x = -1$ into the equation yields $0.$ Solve for $m.$


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