QUADRATIC EQUATIONS AND INEQUATIONS (CDS)

Total Questions: 67

11. Which of the following pair of numbers is the solution of the equation 3ˣ⁺² + 3⁻ˣ = 10 ? [2019 (I) Morning Shift]

Correct Answer: (b) 0, −2
Solution:


12. If x² - 6x - 27 > 0 then which one of the following is correct? [2018 (II) Evening Shift]

Correct Answer: (c) x > 9 or x < - 3
Solution:Given, x² - 6x - 27 > 0

13. If α and ẞ are two real numbers such that α + β = q/p and αβ = where l < p < q < r, then which one of the following is the greatest? [2018 (II) Evening Shift]

Correct Answer: (c)
Solution:


14. Solve the following equation [2018 (II) Evening Shift]

Correct Answer: (a) a/bc
Solution:We have, α, β are the roots of the equation

15. The minimum value of the expression 2x² + 5x + 5 is [2018 (II) Evening Shift]

Correct Answer: (b) 15/8
Solution:Let y = 2x² + 5x + 5 is

16. It is given that equations x² - y² = 0 and (x - a)² + y² = 1 have single positive solution. For this, the value of 'a' is [2018 (II) Evening Shift]

Correct Answer: (a) √2
Solution:We have, x² - y² = 0 ... (i)

17. If α, β and γ are the zeroes of the polynomial f(x) = ax³ + bx² + cx + d then α² + β² + γ² is equal to [2018 (II) Evening Shift]

Correct Answer: (d)
Solution:We have, f(x) = ax³ + bx² + cx + d, α, β, γ are the zero of the given polynomials

18. If the roots of the equation px² + x + r = 0 are reciprocal to each other, then which one of the following is correct? [2018 (I) Morning Shift]

Correct Answer: (b) p = r
Solution:Let the roots of the equation be ‘α’ and ‘β’. According to the question, α = 1/β ... (i)

19. If α and β are the roots of the equation ax² + bx + c = 0, then what is the value of the expression (α + β) (β + 1) ? [2018 (I) Morning Shift]

Correct Answer: (c)
Solution:α and β are the roots of the equation ax² + bx + c = 0

20. The sum of a number and its square is 20. Then, the number is [2018 (I) Morning Shift]

Correct Answer: (a) −5 or 4
Solution:Let the number be x.