Mathematics
Given f(x) = 16x3 - 8x2 + 4x + 7 Assertion (A): When we subtract 1 from f(x), the resulting polynomial is divisible by (2x + 1). Reason (R): = 1. 1. Assertion (A) is true, but Reason (R) is false. 2. Assertion (A) is false, but Reason (R) is true. 3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A). 4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Related Questions
Given f(x) = ax2 + bx + c, a ≠ 0, b, c ∈ R.
Assertion (A): The factorisation of ax2 + bx + c is possible only if its discriminant = b2 - 4ac < 0.
Reason (R): To factorise ax2 + bx + c, split the coefficient of x into two real numbers such that their algebraic sum is b and their product is ac.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Given a polynomial f(x) = 2x3 - 7x2 - 5x + 4
Assertion (A): (x - 1) is not factor of f(x).
Reason (R): f(1) = -6.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Find the remainder when 2x3 - 3x2 + 4x + 7 is divided by
(i) x - 2
(ii) x + 3
(iii) 2x + 1
When 2x3 - 9x2 + 10x - p is divided by (x + 1), the remainder is -24. Find the value of p.