Question
Let 's' represent the sum of the highest root of
equations I and III, and 'r' denote the product of the lowest root of equation I and the highest root of equation II.Determine the new equation if the roots of this equation are 's'and 'r'. Solve the three equations and construct a new equation in variable 'c' (reduced to the lowest possible factor) using roots of equations I, II, and III, following the instructions provided below.Solution
ATQ, 4 - (20/a) + (28/a) = a2 = (4/a2) + (9/a) - 3 7 - (29/a) + (24/a2) = 0 7a2 - 29a + 24 = 0 (7a - 8)(a - 3) = 0 a = 8/7, 3 Equation II b2 - 4b + 2 = 1/8 × (2b - 5) 8b2 - 32b + 16 = 2b - 5 8b2 - 34b + 21 = 0 (4b - 3)(2b - 7) = 0 b = 3/4, 7/2 Equation III, c2 + 10.5 = 17c/2 2c2 - 17c + 21 = 0 (2c - 3)(c - 7) = 0 c = 3/2, 7 s = 3 + 7 = 10 r = (8/7) × (7/2) = 4 New Equation (x - 10)(x - 4) = 0 x2 - 14x + 40 = 0
In the question assuming the given statements to be true, find which of the conclusion(s) among given three conclusions is/are definitely follows and t...
Statement: P ≤ W < O = D ≥ G > T
Conclusions:
I. P ≤ T
II. W < D
Statement: X≤Y<W =Z ≤U<S;S>T ≥V
I. Z≥T
II. Z > X
Statements : C © S * R, U % R $ ZÂ
Conclusions :Â
I. Z $ CÂ
II. U % SÂ
III. U © C
Statements: N = Q < X ≤ L, L > T = G ≥ E
Conclusions:
I. L ≥ Q
II. G > X
III. L > N
Statements: U > H ≥ W; S > T ≥ B; S < H; C ≤ D = U
Conclusions:
I. D > B
II. T < U
III. W ≤ D
Statements: B < C ≥ D; T < G ≥ E; E < C
Conclusions:
I. T < C
II. C > G
III. E < D
In this question, the relation between various elements is shown in the statement. After the statement, two conclusions are given, select a suitable op...
Statements: P # Q @ R & S $ T # W % I, K $ S @ L
Conclusions: I. K # I II. P & T
...Statements : Z < S < W < D; E ≤ C ≤ Y < D; U < T < S ≤ V
Conclusions :
I. V > Z
II. C < U
III. V > E
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