Advertisements
Advertisements
प्रश्न
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Advertisements
उत्तर
If (x – 3) divides f(x) = x3 – px2 + x + 6, then
Remainder = f(3) = 33 – p(3)2 + 3 + 6 = 36 – 9p
If (x−3) divides g(x) = 2x3 – x2 − (p + 3)x – 6, then
Remainder = g(3) = 3(3)3 – 32 − (p + 3)(3) – 6 = 30 - 3p
Now f(3) = g(3)
⇒ 36 – 9p = 30 − 3p
⇒ −6p = −6
⇒ p = 1
APPEARS IN
संबंधित प्रश्न
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
Find the values of a and b in the polynomial f(x) = 2x3 + ax2 + bx + 10, if it is exactly divisible by (x+2) and (2x-1).
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
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
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x5 - a2x3 + 2x + a + 1.
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
When 3x2 – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x2 – 5x + p – 3.
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 (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
