All Exams Test series for 1 year @ ₹349 only
Question

If the roots of the equation x2 - bx + c = 5 differ by 5, then which one of the following is correct ?  

This question was previously asked in
CDS I 2023 English Previous Year Paper (16-April-2023)
The correct answer is

b2 = 4c + 5

Step 1:

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

Step 2:

\(25=b^2-4(c-5)\Rightarrow b^2=4c+5\)

Was this answer helpful?

Similar Questions

  1. Consider a question and two statements:

    Question :

    Does the equation ax 2+ bx + c = 0 have real roots of opposite sign?

    Statement – I : The discriminant D > 0

    Statement – II : c / a > 0

    Which one of the following is correct in respect of the question and the statements?

  2. If the sum as well as the product of the roots of the equation px 2- 6x + q = 0 is 6, then what is (p + q) equal to?

  3. The value of \(\sqrt {1 + \sqrt {1 + \sqrt {1 + \cdots } } }\)

  4. What is the positive value of m for which the roots of the equation 12x 2+ mx + 5 = 0 are in the ratio 3 ∶ 2?

  5. If \(\frac{x}{a} + \frac{y}{b} = a + b\)  and  \(\frac{x}{a^2} + \frac{y}{b^2} = 2\) , then what is  \(\frac{x}{a^2} - \frac{y}{b^2}\)  equal to?

  6. Two numbers p and q are such that the quadratic equation px 2+ 3x + 2q = 0 has – 6 as the sum and the product of the roots. What is the value of (p – q)?

  7. The minimum value of the expression 2x 2+ 5x + 5 is

  8. If α and β are the roots of the equation ax 2+ bx + c = 0, then the value of 1/(aα + b) + 1/(aβ + b) is

  9. What is the sum of all integer values of n for which n 2+ 19n + 92 is a perfect square?

  10. If (b – 6) is one root of the quadratic equation x 2– 6x + b = 0, where b is an integer, then what is the maximum value of b 2?


Important Questions from Quadratic Equation

  1. If \(\rm \left( \frac{x}{x+1} \right)^2 -5 \left( \frac{x}{x+1} \right) +6=0 \) , then the value of  \(\rm \left( 1+\frac{1}{x} \right) \)  is equal to :
  2. If the roots of the equation (q – r)x 2+ (r – p)x + (p – q) = 0 are equal, then which of the following is true?

  3. Number of real roots of the quadratic equation 3x 2+ 4x + 25 = 0 is

  4. The value of m for which one of the root of x 2 - 3x + 2m = 0 is double of the root of x 2 - x + m = 0 is:

  5. If x 2+ 1 = 2x, then find x – \((\frac{1}{x})\)

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
559 Tests 4 Tests Free
1778 Attempts
4.3(192)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App