Advertisements
Advertisements
प्रश्न
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
उत्तर
It is given that `f(x) = 3x^3 + x^3 - 20x + 12` and g(x) = 3x − 2
By the factor theorem,
(3x − 2) is the factor of f(x), if `f(2/3) =0`
Therefore,
In order to prove that (3x − 2) is a factor of f(x).
It is sufficient to show that `f(2/3) =0.`
Now,
`f(2/3) = 3(2/3)^3 + (2/3) ^2 - 20(2/3) +12`
`= 3(8/27) + 4/9 - 40/3 + 12`
` = 8/9 + 4/9 - 40 /3 + 12`
` = 12/9 - 4/3`
` = 4/3 - 4/3`
`= 0`
Hence, (3x − 2) is the factor of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
y3 − 7y + 6
x4 + 10x3 + 35x2 + 50x + 24
If x + 1 is a factor of the polynomial 2x2 + kx, then k =
Factorise the following:
p² – 6p – 16
Factorise the following:
a4 – 3a2 + 2
Factorise:
3x3 – x2 – 3x + 1
