Advertisements
Advertisements
प्रश्न
Find the value of 2x4 + 5x3 + 7x2 − x + 41, if x = `-2 - sqrt(3)"i"`
उत्तर
x = `-2 - sqrt(3)"i"`
∴ x + 2 = `-sqrt(3)"i"`
∴ (x + 2)2 = 3i2
∴ x2 + 4x + 4 = 3(–1) ...[∵ i2 = – 1]
∴ x2 + 4x + 7 = 0 ...(i)
2x2 – 3x + 5
`x^2 + 4x + 7")"overline( 2x^4 + 5x^3 + 7x^2 - x + 41`
2x4 + 8x3 + 14x2
– – –
– 3x3 – 7x2 – x + 41
– 3x3 – 12x2 – 21x
+ + +
5x2 + 20x + 41
5x2 + 20x + 35
– – –
6
Dividend = Divisor x Quotient + Remainder
∴ 2x4 + 5x3 + 7x2 – x + 41
= (x2 + 4x + 7) (2x2 – 3x + 5) + 6
= 0(2x2 – 3x + 5) + 6 ...[From (i)]
= 0 + 6
= 6
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation.
8x2 + 2x + 1 = 0
Solve the following quadratic equation
`2x^2 - sqrt(3)x + 1` = 0
Solve the following quadratic equation.
3x2 − 7x + 5 = 0
Solve the following quadratic equation.
x2 − 4x + 13 = 0
Solve the following quadratic equation.
x2 + 3ix + 10 = 0
Solve the following quadratic equation.
2x2 + 3ix + 2 = 0
Solve the following quadratic equation.
x2 + 4ix − 4 = 0
Solve the following quadratic equation.
ix2 − 4x − 4i = 0
Solve the following quadratic equation.
x2 − (2 + i)x − (1 − 7i) = 0
Solve the following quadratic equation.
`x^2 - (3sqrt(2) +2"i") x + 6sqrt(2)"i"` = 0
Solve the following quadratic equation.
x2 − (5 − i) x + (18 + i) = 0
Solve the following quadratic equation.
(2 + i)x2 − (5 − i) x + 2(1 − i) = 0
Find the value of x3 − x2 + x + 46, if x = 2 + 3i
Find the value of 2x3 − 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Find the value of x3 + x2 − x + 22, if x = `5/(1 - 2"i")`
Find the value of x4 + 9x3 + 35x2 − x + 4, if x = `-5+sqrt(-4)`
Let z be a complex number such that the imaginary part of z is non zero and a = z2 + z + 1 is real. Then a cannot take the value ______
Find the value of x3-x2 , if x=2+3i
Find the value of x3 - x2 + x + 46, if x = 2+3i.
Find the value of x3 - x2 + x + 46, if x = 2 + 3i.
