Answer to Question #21708 in Algebra for Khor Soon Chuan

Question

The heights (in metres) of two men satisfy the quadratic equation 40x^2 - 138x + 119 =0 Without solving the equation, find the average height of these two men.

Answer 1

Let x1, x2 - roots of the equation (and it is heights of two men);we can use Vieta's theorem to find x1+x2.
To do this we can rewrite equation as
x^2-(138/40)*x+119/40=0
Now, from Vieta's theorem x1+x2=-(-138/40)=138/40 averageheight=(x1+x2)/2=138/80=69/40=1.725 metres