Math CentralQuandaries & Queries


Question from abdiwahid, a student:

X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a?

Hi Abdiwahid,

Suppose the root is $r$ then the equation can be written

\[(x - r)(x - r) = 0\]


\[x^2+2ax+4x+9a = (x - r)(x - r).\]

Expand the right side and simplify. This equation is true for all values of $x$ so what does this tell you about $a$ and $r$ when $x = 0?$ This gives you one equation in $a$ and $r.$ Find another equation relating $a$ and $r.$ Solve the two equations for $a.$


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