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Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

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

Option:
A. 5
B. ± 5
C. 0
D. 8
Answer: B . ± 5

Justification:

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

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