Question

If one of the roots of the equation x² - 4 + k = 0 exceeds the other by 2 , then find the roots and determine the value of k.​

Answer 1

Answer:3

Explanation:

Given

Quadratic equation is
`x^2-4+k=0`

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

`=\frac{-\text{coefficient of x}}{\text{coefficient of }x^2}`

`\therefore a+a+2=-(-0)/(1)\\\\\Rightarrow 2a+2=0\\\Rightarrow a=-1`

Product of roots

`\Rightarrow (a)(a+2)=(k-4)/(1)\\\Rightarrow (-1)(1)=k-4\\\Rightarrow k=4-1=3`