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`
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
In the following two polynomials, find the value of a, if x − a is factor x6 − ax5 + x4 − ax3 + 3x − a + 2.
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
If x − 3 is a factor of x2 − ax − 15, then a =
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is
Factorise the following:
y2 – 16y – 80
(x + y)(x2 – xy + y2) is equal to
