math
posted by isha on .
the roots of 2x^2  3x = 4 are a and b. find the simplest quadratic equation which has roots 1/a and 1/b

the sum of the roots of the original is 3/2
the product of the roots is 2
so a+b = 3/2
ab = 2
sum of new roots = 1/a + 1/b = (a+b)/(ab)
= (3/2) / 2 = 3/4
product of new roots  (1/a)(1/b) = 1/(ab) = 1/2
so the new equation is
x^2 + (3/4)x  1/2 = 0 or
4x^2 + 3x  2 = 0
based on the theorem that for
ax^2 + bx + c = 0
the sum of the roots is b/a and
the product of the roots is c/a