Advertisements
Advertisements
प्रश्न
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
Advertisements
उत्तर
It is given that f(x) = 3x4 + 17x3 + 9x2 − 7x − 10 and g(x) = x - 5
By the factor theorem, g(x) is a factor of polynomial f(x)
i.e. x+5 =0
⇒ x= -5
Therefore,
\[f( - 5) = 3 \left( - 5 \right)^4 + 17 \left( - 5 \right)^3 + 9 \left( - 5 \right)^2 - 7\left( - 5 \right) - 10\]
\[ = 3 \times 625 + 17 \times \left( - 125 \right) + 225 + 35 - 10\]
\[ = 1875 - 2125 + 250\]
\[ = 0\]
Hence, g(x) is the factor of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Write the coefficient of x2 in the following:
`9-12x +X^3`
f(x) = x4 − 3x2 + 4, g(x) = x − 2
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
x4 + 10x3 + 35x2 + 50x + 24
If x − 3 is a factor of x2 − ax − 15, then a =
If x + a is a factor of x4 − a2x2 + 3x − 6a, then a =
Factorise the following:
(a + b)2 + 9(a + b) + 18
Factorise the following:
`1/x^2 + 1/y^2 + 2/(xy)`
