Maths (1)

Roots of a quadratic equation ax² + bx +c = 0 are: [- b±√(b² - 4ac)] /2a
sum of roots = [- b +√(b² - 4ac)] /2a + [- b-√(b² - 4ac)] /2a = -b/a

therefore, sum of roots of kx2 – 3x – 10 = 0 is:
-(-3)/k = 2
k = 3/2

Sum of root is, by the equation,
-b/a = -(-3)/k
Therefore, 2=3/k, where k<>0
so, solving the equation,
2k=3, k=3/2

2007-04-05 13:40:05 補充：
For the reason that sum of root =-b/a:By the foundamental theorem of algebra,As it is a quadratic equation, it must have two roots.So a(x-m)(x-n) = 0 , where m,n are two roots.a[x^2-(m+n)x+mn] = 0ax^2 - a(m+n)x + amn = 0So we can see that -a(m+n)=bm+n = -b/aSum of roots = -b/a

solve x using quadratic formula
root 1= {-b+ sqrt[(b^2)-4ac]} / (2a)
root 2= {-b - sqrt[(b^2)-4ac]} / (2a)

root 1 + root 2 = -2b/(2a) = -b/a
a = k, b = -3
3/k = 2
2k = 3
k = 3/2 (or 1.5)