If x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have a common root , then the value of "a" is what ??

If x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have a common root , then

1.	If x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have a common root , then the value of "a" is what ??
Answer» Let the common root be m. Put in the equations; m² + 4am + 3 = 0 --------------(1) 2m² + 3am - 9 = 0 --------------(2) multiply equation (1) by 2 2m² + 8am + 6 = 0 -------------(3) (NOTE that equation 1 and 3 are the same) subtract (2) from (3); you will get (2m² + 8am + 6) - (2m² + 3am - 9) = 0 ⇒ 5am + 15 = 0 ⇒ 5am = -15 ⇒ m = $- \frac{15}{5a} =- \frac{3}{a}$ from equation (1), $(- \frac{3}{a})^{2} + 4a(- \frac{3}{a})+3=0\\ \\ \frac{9}{a^2} - 12+3=0\\ \\ \frac{9}{a^2} -9=0\\ \\\frac{9}{a^2}=9\\ \\a^2= \frac{9}{9}=1\\ \\a=+1\ or\ -1$ So values of a are +1 and -1.