Title 03. Quadratic Equations(Q).pdf ✅

(b) 3x 2 − 10x − 4 = 0 (c) 3x 2 − 10x + 2 = 0 (d) 3x 2 − 20x + 16 = 0 (27 th July 2 nd Shift 2022) 7. If the sum of the squares of the reciprocals of the roots α and β of the equation 3x 2 + λx − 1 = 0 is 15 , then 6(α 3 + β 3 ) 2 is equal to (a) 18 (b) 24 (c) 36 (d) 96 (24 4 th June 1 st Shift 2022) 8. Let a, b ∈ R be such that the equation ax 2 − 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x 2 − 2bx + 21 = 0, then α 2 + β 2 is equal to (a) 37 (b) 58 (c) 68 (d) 92 (25 th June 2 nd Shift 2022) 9. Let α and β be the roots of the equation x 2 + (2i − 1) = 0. Then, the value of |α 8 + β 8 | is equal to : (a) 50 (b) 250 (c) 1250 (d) 1500 (29 9 th June 1 st Shift 2022) 10. If (√3 + i) 100 = 2 99(p + iq), then p and q are roots of the equation (a) x 2 − (√3 + 1)x + √3 = 0 (b) x 2 + (√3 + 1)x + √3 = 0 (c) x 2 + (√3 − 1)x − √3 = 0 (d) x 2 − (√3 − 1)x − √3 = 0 (26 th Aug 2 nd Shift 2021) 11. Let λ ≠ 0 be in R. If α and β are the roots of the equation, x 2 − x + 2λ = 0 and α and γ are the roots of the equation, 3x 2 − 10x + 27λ = 0, then βγ λ is equal to (a) 18 (b) 27 (c) 9 (d) 36 (26 th Aug 2 nd Shift 2021) 12. cosec18∘ is a root of the equation (a) x 2 + 2x − 4 = 0 (b) 4x 2 + 2x − 1 = 0 (c) x 2 − 2x − 4 = 0 (d) x 2 − 2x + 4 = 0 (31 1 st Aug 1 st Shift 2021) 13. If α and β are the distinct roots of the equation x 2 + (3) 1/4x + 3 1/2 = 0, then the value of α 96(α 12 − 1) + β 96(β 12 − 1) is equal to (a) 52 × 3 24