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
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
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.
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
What must be added to x3 − 3x2 − 12x + 19 so that the result is exactly divisibly by x2 + x - 6 ?
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Factorise the following:
z² + 4z – 12
Factorise the following:
p² – 6p – 16
Factorise the following:
(p – q)2 – 6(p – q) – 16
