Question

If 1 and 2 are the zeroes of xpower4+2xpower3-7xpower2+ax+b then find the values of a and b

Answer 1

Let p(X)=x^4+2x^3-7x^2+ax+b
p(1)=1+2-7+a+b=0
a+b=4
p(2)=16+16-28+2a+b=0
2a+b=-4
a+a+b=-4
a+4=-4
a=-8and b=4-a=4-(-8)=12