Advertisements
Advertisements
प्रश्न
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Advertisements
उत्तर
We have been given two polynomials
P(x) = x5 - 4x3 + x2 + 3x + 1 and g(x) = x3 - 3x + 1
We will say g(x) is factor of p(x) if remainder is zero when we divide p(x) by g(x).
x3 -3x + 1)`("x"^2-1)/("x"^5-4"x"^3+"x"^2+3"x"+1)`
`"x"^5-"x"^3+"x"^2`
- + -
-x3 + 3x +1
-x3 + 3x - 1
+ - +
2
Here, the remainder is 2 ≠ 0
g(x) is not a factor of p(x)
Notes
x3 -3x + 1)`("x"^2-1)/("x"^5-4"x"^3+"x"^2+3"x"+1)`
`"x"^5-"x"^3+"x"^2`
- + -
-x3 + 3x +1
-x3 + 3x - 1
+ - +
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]
The number of polynomials having zeroes as –2 and 5 is ______.
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
