Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 - 4x + a be the given polynomials.
When p(x) and q(x) are divided by (x - 3) the remainder are p(3) and q(3) respectively.
p(3) = q(3) given
a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a
⇒ 27a + 36 + 9 - 4 = 27 - 12 + a
⇒ 26a = 15 - 41
⇒ 26a = -26
∴ a = `-(26)/(26)`
= -1.
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.
Using Remainder Theorem, factorise : x3 + 10x2 – 37x + 26 completely.
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:
x4 - a2x2 + 3x - a.
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
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
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
