Advertisements
Advertisements
प्रश्न
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
Advertisements
उत्तर
According to the question,
Let p(x) = x5 – 4a2x3 + 2x + 2a + 3 and g(x) = x + 2a
g(x) = 0
⇒ x + 2a = 0
⇒ x = –2a
Therefore, zero of g(x) = –2a
We know that,
According to the factor theorem,
If g(x) is a factor of p(x), then p(–2a) = 0
So, substituting the value of x in p(x), we get,
p(–2a) = (–2a)5 – 4a2(–2a)3 + 2(–2a) + 2a + 3 = 0
⇒ –32a5 + 32a5 – 2a + 3 = 0
⇒ –2a = –3
⇒ a = `3/2`
APPEARS IN
संबंधित प्रश्न
Write the degrees of the following polynomials:
`12-x+2x^3`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`r(x)=3x^2+4x^2+5x-7`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
x3 − 2x2 − x + 2
Factorize of the following polynomials:
x3 + 13x2 + 31x − 45 given that x + 9 is a factor
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 =
The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is
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:
a4 – 3a2 + 2
