meklitgirma
meklitgirma meklitgirma
  • 01-04-2021
  • Mathematics
contestada

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.​

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nuuk nuuk
  • 06-04-2021

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]

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