Find the values of k ε R subject to the following condition :The diffrenence between th

Find the values of k ε R subject to the following condition :
The diffrenence between the roots of $x^2 + kx + 4 = 0 is 3.$

A. 5

B. ± 5

C. 0

D. 8

E. None of the above

Answer: B. ± 5

Here, If the roots of the equation are α and β (α > β), then α - β = 3
Also, α + β = -k and αβ = $4/1 = 4$
Now, $ (α+ β)^2 = (α - β)^2 + 4αβ$
.`. $k^2 = 9 + 4(4)$
.`. $k^2 = 25$
.`. k = ±5

Posted in: Quadratic Equations - Algebra - Mathematics

Find the values of k ε R subject to the following condition :The diffrenence between the roots of $x^2 + kx + 4 = 0 is 3.$

Find the values of k ε R subject to the following condition :
The diffrenence between the roots of $x^2 + kx + 4 = 0 is 3.$