If A and B are the roots of the quadratic equation, 3 x^2-10 x-25=0 then the value of 3 ^2(A+B)-10 (A+B) (A+B)-25 ^2(A+B) is

Step-by-step solution

As A and B are the roots of 3 x^2-10 x-25=0 So, (A+B)= A+ B 1- A B = 10 3 1+ 25 3 = 10 / 3 28 / 3 = 5 14 Now, ^2(A+B)=-1+2 ^2(A+B)= 1- ^2(A+B) 1+ ^2(A+B) ^2(A+B)= 196 221 3 ^2(A+B)-10 (A+B)= ^2(A+B) [3 ^2(A+B)-10 (A+B)-25 ]= 75-700-4900 196 196 221 =- 5525 196 196 221 =-25