Advertisements
Advertisements
प्रश्न
If x + a is a factor of x4 − a2x2 + 3x − 6a, then a =
विकल्प
0
-1
1
2
Advertisements
उत्तर
As (x +a) is a factor of polynomial f(x) = x4 − a2x2 + 3x − 6a,
Therefore,
f(-a) = 0
`(-a)^4 - a^2 (-a)^2 +3(-a) - 6a = 0`
`a^4 - a^4 - 3a - 6a =0`
`a =0`
APPEARS IN
संबंधित प्रश्न
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
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 \[x - \frac{1}{2}\].
In the following two polynomials, find the value of a, if x − a is factor x6 − ax5 + x4 − ax3 + 3x − a + 2.
Find the values of p and q so that x4 + px3 + 2x3 − 3x + q is divisible by (x2 − 1).
x3 + 2x2 − x − 2
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
Factorise the following:
`1/x^2 + 1/y^2 + 2/(xy)`
