Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
उत्तर
Let `f(x) = x^5 - a^2 x^3 + 2x + a `+1 be the given polynomial.
By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.
Therefore,
`⇒ f(a) = (a)^5 - a^2(a)^3 + 2 (a) + a + 1 = 0`
`a^5 - a^5 + 2a + a+1 = 0`
`3a + 1 = 0`
` a= (-1)/3`
Thus, the value of a is − 1/3.
APPEARS IN
संबंधित प्रश्न
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 5 + 2x .
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.
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
What must be added to x3 − 3x2 − 12x + 19 so that the result is exactly divisibly by x2 + x - 6 ?
x3 − 10x2 − 53x − 42
x3 − 2x2 − x + 2
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Factorise the following:
6x2 + 16xy + 8y2
