Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
Advertisements
उत्तर
Let f(x) = x3 + ax2 − 2x +a + 4 be the given polynomial.
By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^3 + a(-a)^2 -2(-a) + a + 4 = 0`
`-a^3 + a^3 2a + a + 4 = 0`
`3a + 4 = 0`
`a = (-4)/3`
Thus, the value of a is − 4/3.
APPEARS IN
संबंधित प्रश्न
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
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
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 case, if R1 + R2 = 0.
y3 − 2y2 − 29y − 42
x3 + 13x2 + 32x + 20
2y3 + y2 − 2y − 1
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively
Factorise the following:
9 – 18x + 8x2
