All the values of k for which the quadratic polynomial f(x)=−2x2+kx+k2+5 has two distinct zeroes and only one of them satisfying 0

For two distinct roots, D>0 i.e., k2+8k2+5>0which is always trueAlso let f(x)=−2x2+kx+k2+5=0But f(0)>0 and f(2)<0    −8+2k+k2+5<0 ⇒ k2+2k−3<0⇒     (k+3)(k−1)<0    k∈(−3,1)⇒a=−3;b=1⇒     a3+b3=−26