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
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.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
(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.
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
