Mathematics
If mx2 - nx + 8 has x - 2 as a factor, then :
2m - n = 4
2m + n = 4
2n + m = 4
n - 2m = 4
Answer
By factor theorem,
If x - a is the factor of polynomial f(x), then remainder f(a) = 0.
Given,
x - 2 is a factor of mx2 - nx + 8.
Then substituting x = 2 in polynomial we get, remainder = 0 :
⇒ m(2)2 - 2n + 8 = 0
⇒ 4m - 2n + 8 = 0
⇒ 2(2m - n + 4) = 0
⇒ 2m - n + 4 = 0
⇒ n - 2m = 4.
Hence, Option 4 is the correct option.
Related Questions
Is (x - 2) a factor of x3 - 4x2 - 11x + 30 ?
yes
no
nothing can be said
none of the above is true
4x2 - kx + 5 leaves a remainder 2 when divided by x - 1. The value of k is :
-6
6
7
-7
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.
The polynomial 3x3 + 8x2 - 15x + k and one of its factors as (x - 1).
Assertion (A) : The value of k = 4.
Reason (R) : x - 1 = 0 ⇒ x = 1.
∴ 3.(1)3 + 8.(1)2 - 15 x (1) + k = 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.