Advertisements
Advertisements
प्रश्न
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x3 + ax2 − 2x + a + 4
Find the value of a if x + a is a factor of x3 + ax2 − 2x + a + 4.
Advertisements
उत्तर
Let p(x) = x3 + ax2 − 2x + a + 4 ...(i)
Since, (x + a) is a factor of p(x),
So p(−a) = 0
Put x = −a in equation (i), we get
p(−a) = (−a)3 + a(−a)2 − 2(−a) + a + 4
= −a3 + a(a2) + 2a + a + 4
= −a3 + a3 + 3a + 4
= 3a + 4
But p(−a) = 0
⇒ 3a + 4 = 0
⇒ 3a = −4
⇒ a = `−4/3`
APPEARS IN
संबंधित प्रश्न
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
If the polynomials ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x6 - ax5 + x4 - ax3 + 3a + 2
If (x – 2) is a factor of 2x3 – x2 + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely
While factorizing a given polynomial using the remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student’s solution correct in stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
