SEARCH HOME
 Math Central Quandaries & 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

$(x - r)(x - r) = 0$

so

$x^2+2ax+4x+9a = (x - r)(x - r).$

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 $a.$

Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.