Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Advertisements
उत्तर
Let f(x) = 3x3 + 10x2 + x – 6
For x = –1,
f(x) = f(–1)
= 3(–1)3 + 10(–1)2 + (–1) – 6
= –3 + 10 – 1 – 6
= 0
Hence, (x + 1) is a factor of f(x).
3x2 + 7x – 6
`x + 1")"overline(3x^3 + 10x^2 + x - 6)`
3x3 + 3x2
– –
7x2 + x
7x2 + 7x
– –
– 6x – 6
– 6x – 6
+ +
0
∴ 3x3 + 10x2 + x – 6 = (x + 1)(3x2 + 7x – 6)
= (x + 1)(3x2 + 9x – 2x – 6)
= (x + 1)[3x(x + 3) – 2(x + 3)]
= (x + 1)(x + 3)(3x – 2)
Now, 3x3 + 10x2 + x – 6 = 0
(x + 1)(x + 3)(3x – 2) = 0
`x = -1, -3, 2/3`
APPEARS IN
संबंधित प्रश्न
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
