If (a-b/2)x²-(a+b/2)x+b=0 then what are the roots of this equation?

Correct Answer is : 1,2ba−b1,2b/a-b1,a−b2b

Correct Answer is : 1,2ba−b1,2b/a-b1,a−b2b

Test Index

UPSC CDS II 2025 Mathematics Paper

Question : 25 of 100

Marks: +1, -0

(\frac{a-b}{2})x^{2}-(\frac{a+b}{2})x+b=0

then what are the roots of this equation?

Solution:

Concept:

The given quadratic equation is solved by checking a possible root and using the sum of roots formula.

Explanation:

Multiply the entire equation by 2 to clear denominators.

(a-b)x^{2}-(a+b)x+2b=0

Test

x=1

(a-b)-(a+b)+2b = a-b-a-b+2b=0

, so 1 is a root.

For a quadratic

Ax^{2}+Bx+C=0

, sum of roots

= -B/A = \frac{a+b}{a-b}

Let the other root be

r

. Then

1+r = \frac{a+b}{a-b}

Solve:

r = \frac{a+b}{a-b} - 1 = \frac{a+b - (a-b)}{a-b} = \frac{2b}{a-b}

Thus the roots are

1

and

\frac{2b}{a-b}

Answer:

1,\frac{2b}{a-b}

(Option B)

Go to Question:

Prev Question

Next Question