QUADRATIC EQUATIONS AND INEQUATIONS (CDS)

Total Questions: 67

1. If the equations x² + 5x + 6 = 0 and x² + kx + l = 0 have a common root, then what is the value of k ? [2019 (II) Evening Shift]

Correct Answer: (b)
Solution:Given, equations


2. The sum of the squares of four consecutive natural numbers is 294. What is the sum of the numbers? [2019 (II) Evening Shift]

Correct Answer: (b) 34
Solution:Let the four consecutive natural numbers are x - 1, x + 1, x + 2

3. The equation x² + px + q = 0 has roots equal to p and q where q ≠ 0. What are the values of p and q, respectively? [2019 (II) Evening Shift]

Correct Answer: (a) 1, - 2
Solution:x² + px + q = 0

4. How many pairs of natural numbers are there such that the difference of their squares is 35? [2019 (II) Evening Shift]

Correct Answer: (b) 2
Solution:Let the number be x and y.


5. If (b − 6) is one root of the quadratic equation x² -6x + b = 0, where b is an integer, then what is the maximum value of b² ? [2019 (II) Evening Shift]

Correct Answer: (d) 81
Solution:(b − 6) is one root of expression

6. What is the maximum value of [2019 (II) Evening Shift]

Correct Answer: (d)
Solution:


7. Two numbers p and q are such that the quadratic equation px² + 3x + 2q = 0 has −6 as the sum and the product of the roots. What is the value of (p − q) ? [2019 (II) Evening Shift]

Correct Answer: (c) 2
Solution:px² + 3x + 2q = 0

8. Given that the polynomial (x² + ax + b) leaves the same remainder when divided by (x − 1) or (x + 1). What are the values of a and b, respectively? [2019 (I) Morning Shift]

Correct Answer: (d) 0 and any integer
Solution:


9. If p and q are the roots of the equation x² - 15x + r = 0 and p - q = 1 then what is the value of r? [2019 (I) Morning Shift]

Correct Answer: (b) 56
Solution:p and q are the roots of the equation.

10. For the inequation x² - 7x + 12 > 0 which one of the following is correct? [2019 (I) Morning Shift]

Correct Answer: (d) - ∞ < x < 3 or 4 < x < ∞
Solution: