Mathematics — MCQ Practice Questions & Answers

Question 1

If α and β are roots of 3x² - 4x + k = 0 and α² + β² = 10/9, then k equals:

Accepted Answer

Correct answer: C. 1/3 — From Vieta's formulas: α + β = 4/3 and αβ = k/3. Using α² + β² = (α+β)² - 2αβ, we get 10/9 = (4/3)² - 2(k/3) = 16/9 - 2k/3. Solving: 10/9 = 16/9 - 2k/3 gives 2k/3 = 6/9 = 2/3, so k = 1/3.

Answer

A. 1

Answer

B. 2/3

Answer

D. 4/3

Question 2

If a, b, c are in geometric progression with common ratio r, and a + b + c = 39, while a² + b² + c² = 651, then the value of r is:

Accepted Answer

Correct answer: B. 2 — In GP: b = ar and c = ar². Given a + ar + ar² = 39 and a² + a²r² + a²r⁴ = 651. From the first equation: a(1 + r + r²) = 39. From the second: a²(1 + r² + r⁴) = 651. Dividing these equations and solving yields r = 2, which satisfies both conditions when a = 3.

Answer

A. 1/2

Answer

C. 3

Answer

D. 1/3

Mathematics - MCQ Practice Questions