For a quadratic polynomial , the sum of the zeroes is . Here, . Thus, sum = = .
82. If two lines are parallel, their system of equations has
(a) One solution
(b) No solution
(c) Infinite solutions
(d) Exactly two solutions
Answer:
(b) No solution
Explanation:
Parallel lines never intersect on a Cartesian plane, meaning there are no points that satisfy both linear equations simultaneously.
83. For , the value of the discriminant is given by
(a)
(b)
(c)
(d)
Answer:
(a)
Explanation:
The discriminant determines the nature of the roots of a quadratic equation and is calculated using the formula .
84. Which of the following is not an A.P. ?
(a) 1, 4, 7, …
(b) 3, 7, 12, 18, …
(c) 11, 14, 17, 20, …
(d) -5, -2, 1, 4, …
Answer:
(b) 3, 7, 12, 18, …
Explanation:
An Arithmetic Progression (A.P.) requires a constant common difference between consecutive terms. In (b), the differences are 4 (7-3), 5 (12-7), and 6 (18-12). Since the difference is not constant, it is not an A.P.
85. What is the value of ?
(a)
(b)
(c)
(d)
Answer:
(b)
Explanation:
By standard trigonometric ratios, the sine of 60 degrees is .