Q&A Let p(x) be a cubic polynomial with integer coefficients with leading coefficient 1 and with one of its roots equal to the product of the other two. Show that 2p(−1) is a multiple of p(1) + p(−1) − 2(1 + p(0))

Q&A The product of two of the four roots of the quartic equation x^4 − 18x^3 + kx^2 + 200x − 1984 = 0 is −32. Determine the value of k.

Multiple choice The condition for the polynomial equation of degree 4 ax^4+bx^2+c=0 to have four distinct real roots is

Multiple choice p^2\geq 4q is the condition for the biquadratic equation x^4+px^2+q=0 to have real roots.

Q&A If a,b are real numbers such that\sqrt{\dfrac{a}{b} } +b=7 \sqrt{\dfrac{b}{a} } +a=11find the values of a,b

Multiple choice Let f (x) = ax^2 and g(x) = bx^4 for any value of x. If a and b are positive constants, for how many values of x is f (x) = g(x) ?