Let 30^ and 15^ be the roots of the quadratic equation x^2+a x+b=0 , then 1+a-b=

Step-by-step solution

aligned & 15^ = (45^ -30^ ) & = 1-1 / 3 1+1 / 3 = 3 -1 3 +1 . aligned Given, 30^ and 15^ are the roots of the equation x^2+a x+b=0 Sum of roots = 30^ + 15^ =-a aligned & 1 3 + 3 -1 3 +1 =-a & 3 +1+3- 3 3 ( 3 +1) =-a a= -4 3 ( 3 +1) aligned Now, product of roots = 30^ 15^ =b b= 1 3 3 -1 3 +1 Now, we have to find 1+a-b . Then, 1+a-b=1- 4 3 ( 3 +1) - 3 -1 3 ( 3 +1) = 3 ( 3 +1)-4- 3 +1 3 ( 3 +1) = 3+ 3 -3- 3 3 ( 3 +1) =0