If the roots of the equation x² - nx + m = 0, Differ by 1, then

Correct Answer is : n2−4m−1=0n² - 4m - 1 = 0n2−4m−1=0

Correct Answer is : n2−4m−1=0n² - 4m - 1 = 0n2−4m−1=0

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UPSC NDA II 2015 Mathematics Paper

Question : 51 of 120

Marks: +1, -0

x^{2} - nx + m = 0

, Differ by 1, then

Solution:

Concept:

For a quadratic equation

ax^2+bx+c=0

, the sum of roots is

\frac{-b}{a}

and the product is

\frac{c}{a}

Explanation:

The given equation is

x^2-nx+m=0

Here

a=1

b=-n

c=m

Let the roots be

\alpha

and

\beta

Then

\alpha+\beta=n

and

\alpha\beta=m

The roots differ by 1, so

\alpha-\beta=1

Use the identity

(\alpha+\beta)^2 = (\alpha-\beta)^2 + 4\alpha\beta

Substitute the known values:

n^2 = 1^2 + 4m

Simplify to

n^2 - 4m - 1 = 0

Answer:

Option A:

n^2 - 4m - 1 = 0

is correct.

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