Advertisements
Advertisements
प्रश्न
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
उत्तर
Let f(x) = 2x3 + 3x2 – kx + 5
Using remainder theorem,
f(2) = 7
∴ 2(2)3 + 3(2)2 – k(2) + 5 = 7
`\implies` 2(8) + 3(4) – k(2) + 5 = 7
`\implies` 16 + 12 – 2k + 5 = 7
`\implies` 2k = 16 + 12 + 5 – 7
`\implies` 2k = 26
`\implies` k = 13
संबंधित प्रश्न
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
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.
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
