Can a quadratic polynomial `x^2 + kx + k` have equal zeros for some odd integer `k gt 1`?

Answer the following and justify. (i) can x^(2)-1 be the quotient on division of x^(6) +2x^(3) +x - 1 by a polynomial in x of degree 5? (ii) What will be quotient and remainder be on division of ax^(2)+bx +c by px^(3) +qx^(2) +rx +s, p ne 0 ? (iii) If on division of a polynomial p(x) by a polynomial g(x) , the quotient is zero, what is the relation between the degree of p(x) and g(x) ? (iv) If on division of a non-zero polynomial p(x) by a polynomial g(x) , the remainder is zero, what is the relation between the degrees of p(x) and g(x) ? (v) Can be quadratic polynomial x^(2) +kx +k have equal zeroes for some odd integer k gt 1 ?

If the sum of the zeros of the quadratic polynomial kx^(2)+2x + 3k is equal to the product of its zeros then k = ?

What is the value of k in the quadratic polynomial kx^2 + 4x + 3k , if the sum of the zeroes is equal to their product ?

What is the value of k in the quadratic polynomial kx^(2) + 4x + 3k , if the sum of the zeroes is equal to their product?

The zeroes of the quadratic polynomial x^(2) +kx +k where k ne 0 ,

Find the value of k if the quadratic polynomial p(x)=x^2+8x+k has zeroes whose difference is 4

If one zero of the quadratic polynomial p(x) = x^2 + 4kx – 25 is negative of the other, find the value of k.

If one of the zeros of the quadratic polynomial f(x) = 4x^2 - 8kx - 9 is equal in magnitude but opposite in sign of the other, find the value of k.

Find the quadratic polynomial having zeroes -1 and 2

Assertion (A): Both zeroes of the quadratic polynomial x^(2)-2kx+2 are equal in magnitude but opposite in sign then value of k is 1/2 . Reason(R):Sum of zeroes of a quadratic polynomial ax^(2)+bx+c is (-b)/a