Question

Question1 (v)
Answer the following and justify
v) Can the quadratic polynomial $x^2+kx+k$ have equal zeroes for some odd integer k > 1?

Answer 1

v) No, let p (x) = x2 + kx + k
if p (x) has equal zeroes, then its discriminate should be zero
$\therefore$ $D=B2–4AC=0$
On comparing p (x) with $A{x}^2+Bx+C$, we get
On comparing p (x) with $Ax2+BX+C$, we get
A = 1, B = k and C = k
$\therefore (k{)}^2–4(1\left)\right(k)=0$
$\Rightarrow k(k–4)=0$
$\Rightarrow k(k–4)=0$
$\Rightarrow k=0,4$
So, he quadratic polynomial p(x) have equal zeroes only at k = 0, 4