Exams › IBPS PO › Quantitative Aptitude

Directions (141-143): Solve the given equations and answer the question below. I. \(Ax^2 + 5x + 6 = 0\) II. \(By^2 - 13y + 20 = 0\) III. \(u^2 + 7u + 12 = 0\) IV. \(v^2 - 9v + 20 = 0\) Note: (i) The sum of the coefficients of \(x^2\), \(x\), \(y^2\), and \(y\) is -5. (ii) Roots of all the equations are non-imaginary. (iii) Both A and B are positive integers. Find the difference between the larger root of equation IV and the smaller root of equation II.

1. 2.5
2. 4
3. 1.5
4. 2
5. 3.5

Correct answer: 2.5

Solution

The coefficient-sum condition gives \(A+5+B-13=-5\), so \(A+B=3\). Since A and B are positive integers and roots are real, the valid values are determined accordingly. Then equation II and IV can be solved to get the required roots, whose difference is 2.5.

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