For expression f(x)=x3+ax2+bx+c if f(1)=f(2)=0 and f(4)=f(0), then the value of a,b and c - Maths - Polynomials

Question

For expression f(x)=x3+ax2+bx+c if
f(1)=f(2)=0 and f(4)=f(0), then the value of a,b and c

Anuradha Sharma · Accepted Answer

Dear Student, f1= f2=0 and f4=f0, so a+b+c=-1
14a+2b+c=-8 216a+4b+c+64=c4a+b= -16
3Subtracting, equation 1 and 2, 3a+b=-7
4SUbtracting equation 3 and 4, a = -9SO b = -7-3×-9=20Now from equation 1, c = -1+9-20=-12Regards