Advertisements
Advertisements
प्रश्न
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Advertisements
उत्तर
It is given that f(x) = 2x3 − 9x2 + x + 12 and g(x) = (3 − 2x)
By factor theorem, (3 − 2x) is the factor of f(x), if f(3/2)= 0
Therefore,
In order to prove that (3 − 2x) is a factor of f(x). It is sufficient to show that `f(3/2) = 0`
Now,
`f(3/2) = 2(3/2)^3 -9(3/2)^2 +(3/2) + 12`
` = 27/4 - 81/4 + 3/2 + 12`
` = 54 / 4 + 3/2 + 12`
` = -27/2 + 3/2 +12`
` = -12 + 12`
`= 0`
Hence, (3 − 2x), is the factor of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)
f(x) = x3 + 4x2 − 3x + 10, g(x) = x + 4
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
x3 − 6x2 + 3x + 10
y3 − 2y2 − 29y − 42
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
Factorise the following:
y2 – 16y – 80
Factorise the following:
(a + b)2 + 9(a + b) + 18
