Tiêu đề 03. Quadratic Equations(Q).pdf ✅

(b) 56 × 3 25 (c) 28 × 3 25 (d) 56 × 3 24 (20 th July 1 st Shift 2021) 14. Let α, β be two roots of the equation x 2 + (20) 1/4x + (5) 1/2 = 0. Then α 8 + β 8 is equal to (a) 50 (b) 160 (c) 100 (d) 10 (27 th July 1 st Shift 2021) 15. Let α = max x∈R {8 2sin3x ⋅ 4 4cos 3x } and β = minx∈R {8 2sin3x ⋅ 4 4cos 3x } If 8x 2 + bx + c = 0 is a quadratic equation whose roots are α 1 5 and β 1 5, then the value of c − b is equal to (a) 43 (b) 42 (c) 50 (d) 47 (27 7 th July 2 nd Shift 2021) 16. Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be ( 10 3 , 7 3 ). If α, β are the roots of the equation ax 2 + bx + 1 = 0, then the value of α 2 + β 2 − αβ is (a) − 71 256 (b) 71 256 (c) − 69 256 (d) 69 256 (24 th Feb 2 nd Shift 2021) 17. If α, β ∈ R are such that 1 − 2i (here i 2 = −1 ) is a root of z 2 + αz + β = 0, then (α − β) is equal to (a) -3 (b) -7 (c) 7 (d) 3 (25 5 th Feb 2 nd Shift 2021) 18. Let f(x) be a quadratic polynomial such that (−1) +f(2) = 0. If one of the roots of f(x) = 0 is 3 , then its other root lies in (a) (1,3) (b) (−3, −1) (c) (0,1) (d) (−1,0) ( 2 nd Sept 1 st Shift 2020) 19. Let α and β be the roots of the equation, 5x 2 + 6x − 2 = 0. If Sn = α n + β n , n = 1,2,3, ..., then (a) 6S6 + 5S5 = 2S4 (b) 6S6 + 5S5 + 2S4 = 0 (c) 5S6 + 6S5 = 2S4 (d) 5S6 + 6S5 + 2S4 = 0 (2 2 nd Sept 1 st Shift 2020)