Mathematics
4x2 - kx + 5 leaves a remainder 2 when divided by x - 1. The value of k is :
-6
6
7
-7
Answer
By remainder theorem,
If polynomial ƒ(x) is divided by (x - a) then the remainder will be ƒ(a).
Given,
4x2 - kx + 5 leaves a remainder 2 when divided by x - 1.
∴ 4(1)2 - k(1) + 5 = 2
⇒ 4(1) - k + 5 = 2
⇒ 4 - k + 5 = 2
⇒ 9 - k = 2
⇒ k = 9 - 2 = 7.
Hence, Option 3 is the correct option.
Related Questions
If x - 3 is a factor of x2 + kx + 15; the value of k is :
8
3
-5
-8
Is (x - 2) a factor of x3 - 4x2 - 11x + 30 ?
yes
no
nothing can be said
none of the above is true
If mx2 - nx + 8 has x - 2 as a factor, then :
2m - n = 4
2m + n = 4
2n + m = 4
n - 2m = 4
Two polynomials x36 - 3x35 and x - 3.
Assertion (A) : If x - 3 is a factor of x36 - 3x35, the remainder is zero.
Reason (R) : The polynomial x - a is factor of polynomial p(x) = x36 - ax35, if p(a) = 0
options
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.