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 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
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’.
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
