Advertisements
Advertisements
प्रश्न
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
Advertisements
उत्तर
Let 3x – 2 = 0,
then 3x = 2
⇒ x = `(2)/(3)`
Substituting the value of x in f(x),
f(x) = 3x3 – kx2 + 21x – 10
`f(2/3) = 3(2/3)^3 - k(2/3)^2 + 21(2/3) - 10`
= `3 xx (8)/(27) - k xx (4)/(9) + 21 xx (2)/(3) - 10`
= `(8)/(9) - (4k)/(9) + 14 - 10`
= `(8 - 4k)/(9) + 4`
∵ Remainder is 0
`(8 - 4k)/(9) + 4` = 0
⇒ 8 – 4k + 36 = 0
⇒ –4k + 44 = 0
⇒ 4k = 44
∴ k = 11.
APPEARS IN
संबंधित प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
