Advertisements
Advertisements
प्रश्न
Verify division algorithm for the polynomial `f(x)= (8 + 20x + x^2 – 6x^3) by g(x) =( 2 + 5x –3x^2).`
उत्तर
We can write f(x) as –`6x^3 + x^2 + 20x + 8 and g(x)` as `–3x^2 + 5x + 2`
Quotient = 2x + 3
Remainder = x + 2
By using division rule, we have
Dividend = Quotient × Divisor + Remainder
∴` –6x^3 + x^2 + 20x + 8 = (–3x^2 + 5x + 2) (2x + 3) + x + 2`
⇒` –6x^3 + x^2 + 20x + 8 = –6x^3 + 10x^2 + 4x –9x^2 + 15x + 6 + x + 2`
⇒` –6x^3 + x^2 + 20x + 8 = –6x^3 + x^2 + 20x + 8 `
APPEARS IN
संबंधित प्रश्न
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
p(x) = x4 – 5x + 6, g(x) = 2 – x2
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 10x4 + 17x3 − 62x2 + 30x − 3, g(x) = 2x2 + 7x + 1
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = 2x2 − x + 3, f(x) = 6x5 − x4 + 4x3 − 5x2 − x − 15
Find all the zeros of the polynomial x4 + x3 − 34x2 − 4x + 120, if two of its zeros are 2 and −2.
Find all the zeros of the polynomial x3 + 3x2 − 2x − 6, if two of its zeros are `-sqrt2` and `sqrt2`
If (a-b) , a and (a + b) are zeros of the polynomial `2x^3-6x^2+5x-7` write the value of a.
If `x^3+ x^2-ax + b` is divisible by `(x^2-x)`,write the value of a and b.
Find the quotient and remainder of the following.
(−18z + 14z2 + 24z3 + 18) ÷ (3z + 4)
The sum of (x + 5) observations is (x3 + 125). Find the mean of the observations
Given that `x - sqrt(5)` is a factor of the cubic polynomial `x^3 - 3sqrt(5)x^2 + 13x - 3sqrt(5)`, find all the zeroes of the polynomial.
