Advertisements
Advertisements
प्रश्न
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
उत्तर
p(x) = x3 – 3x2 – mx + 24
when x + 3 is a factor
P(–3) = 0
(–3)3 – 3(–3)2 – m(–3) + 24 = 0
– 27 – 27 + 3m + 24 = 0
– 54 + 24 + 3m = 0
– 30 + 3m = 0
3m = 30
m = `30/3`
= 10
The value of m = 10
APPEARS IN
संबंधित प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
