Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let f(x) = x5 − 3x4 − ax3 + 3ax2 + 2ax + 4 be the given polynomial.
By the factor theorem, (x − 2) is a factor of f(x), if f (2) = 0
Therefore,
`f(2) = (2)^3 - 3(2)^4 - a(2)^3 + 3a(2)^2 + 4 = 0 `
`32 - 48 - 8a + 12a + 4a + 4 = 0`
` - 12 + 8a = 0`
` a = 3/2`
Thus, the value of a is 3/2.
APPEARS IN
संबंधित प्रश्न
Write the coefficient of x2 in the following:
`17 -2x + 7x^2`
Write the coefficient of x2 in the following:
`sqrt3x-7`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials
`p(x)=2x^2-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 value of the following case, if R1 = R2.
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
If x + 2 is a factor of x2 + mx + 14, then m =
Which of the following has x – 1 as a factor?
