let y=x^{2}

Your equation is

If you solve this equation for y the value of x will be So y is greater than or equal to zero if the roots are to be zero.

If the roots are distinct

is not a root and is not equal to zero

Find the range of values of k so that one root is below -4 and the others are above -1 and express that range as a proportion of (-5,5) to get a probability.