Advertisements
Advertisements
प्रश्न
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
Advertisements
उत्तर
Let f(x) = 2x3 + ax2 + bx – 2
2x – 3 = 0 `\implies x = 3/2`
On dividing f(x) by 2x – 3, it leaves a remainder 7.
∴ `2(3/2)^3 + a(3/2)^2 + b(3/2) - 2 = 7`
`27/4 + (9a)/4 + (3b)/2 = 9`
`(27 + 9a+ 6b)/4 = 9`
27 + 9a + 6b = 36
9a + 6b – 9 = 0
3a + 2b – 3 = 0 ...(1)
x + 2 = 0 `\implies` x = –2
On dividing f(x) by x + 2, it leaves a remainder 0.
∴ 2(–2)3 + a(–2)2 + b(–2) – 2 = 0
–16 + 4a – 2b – 2 = 0
4a – 2b – 18 = 0 ...(2)
Adding (1) and (2), we get,
7a – 21 = 0
a = 3
Subsituting the value of a in (1), we get,
3(3) + 2b – 3 = 0
9 + 2b – 3 = 0
2b = –6
b = –3
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.
