Question

1)On dividing 3x3+4x2+5x-13 by a polynomial g(x) the quotient and remainder were 3x+10 and 16x-43 find the polynomial g(x)
2)Form a quadratic polynomial whose zeros are 5+ root 3 and 5- root 3
3)If alpha and beta are the zeros of the polynomial p(x)=2x2-5x+7 find a polynomial whose zeros are root 5 and - root five

Answer 1

By the division algorithm f(x)=q(x) X g(x)+ r(x) g(x) X q(x) = f(x)-r(x) g(x)(3x+10) = 3x3 + 4x2+5x-13 – (16x+43)  g(x)(3x+10) = 3x3 + 4x2+5x-13 –16x-43 g(x)(3x+10)= 3x3+ 4x2-11x+30 g(x) = 3x3 + 4x2-11x+30 / 3x+10       g(x) = x2-2x+3 1 answer