Answer:3
Step-by-step explanation:
Given
Quadratic equation is [tex]x^2-4+k=0[/tex]
if one root exceeds the other by two
suppose one of the roots is a, then the other is a+2
The Sum of roots is
[tex]=\dfrac{-\text{coefficient of x}}{\text{coefficient of }x^2}[/tex]
[tex]\therefore a+a+2=-\dfrac{-0}{1}\\\\\Rightarrow 2a+2=0\\\Rightarrow a=-1[/tex]
Product of roots
[tex]\Rightarrow (a)(a+2)=\dfrac{k-4}{1}\\\Rightarrow (-1)(1)=k-4\\\Rightarrow k=4-1=3[/tex]
