(2x+5)(−mx+9)=0

Question

In the equation above, mmm is a constant. If the equation has the solutions x=-\dfrac{5}{2}x=− 2 5 ​ x, equals, minus, start fraction, 5, divided by, 2, end fraction and x=\dfrac{3}{2}x= 2 3 ​ x, equals, start fraction, 3, divided by, 2, end fraction , what is the value of mmm?

Answer 1

set each factor = 0m,m and solve for x

2x+5 = 0, x = -5/2

-mx+9= 0

mx = 9

x = 9/m

m=9/x where x could = any real number except zero

IF x = 5/2, then m = 9/5/2 = 9(2/5) = 18/5 = 3.6