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
Write the coefficient of x2 in the following:
`pi/6x^2- 3x+4`
If `f(x)=2x^2-13x^2+17x+12` find `f-(3)`
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following cases, if 2R1 − R2 = 0.
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
If x − 2 is a factor of the following two polynomials, find the values of a in each case x5 − 3x4 − ax3 + 3ax2 + 2ax + 4.
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
If x − 3 is a factor of x2 − ax − 15, then a =
Factorise the following:
p² – 6p – 16
(x + y)(x2 – xy + y2) is equal to
