Advertisements
Advertisements
Question
If mx2 – nx + 8 has x – 2 as a factor, then ______.
Options
2m – n = 4
2m + n = 4
2n + m = 4
n – 2m = 4
Advertisements
Solution
If mx2 – nx + 8 has x – 2 as a factor, then n – 2m = 4.
Explanation:
Let f(x) = mx2 – nx + 8
Given x – 2 is a factor of f(x).
Then f(2) = 0
`\implies` m × 22 – n × 2 + 8 = 0
`\implies` 4m – 2n + 8 = 0
`\implies` 2m – n + 4 = 0
`\implies` n – 2m = 4
APPEARS IN
RELATED QUESTIONS
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
