Advertisements
Advertisements
प्रश्न
If mx2 – nx + 8 has x – 2 as a factor, then ______.
विकल्प
2m – n = 4
2m + n = 4
2n + m = 4
n – 2m = 4
Advertisements
उत्तर
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
संबंधित प्रश्न
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
If (x - 2) is a factor of the expression 2x3 + ax2 + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
x – 1 is a factor of 8x2 – 7x + m; the value of m is ______.
