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
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
x3 − 10x2 − 53x − 42
If x − 3 is a factor of x2 − ax − 15, then a =
If both x − 2 and \[x - \frac{1}{2}\] are factors of px2 + 5x + r, then
Factorise the following:
`sqrt(5)"a"^2 + 2"a" - 3sqrt(5)`
Factorise the following:
`1/x^2 + 1/y^2 + 2/(xy)`
Which of the following has x – 1 as a factor?
Factorise:
x3 + x2 – 4x – 4
