Advertisements
Advertisements
प्रश्न
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
Advertisements
उत्तर
`f(x) as x^4 + 0x^3 + 0x^2 – 5x + 6 and g(x) as – x^2 + 2`
Quotient q(x) = `– x^2 – 2`
Remainder r(x) = –5x + 10
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
If α and β are the zeros of the quadratic polynomial f(x) = 6x2 + x − 2, find the value of `alpha/beta+beta/alpha`.
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
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 the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
Verify that 5, -2 and 13 are the zeroes of the cubic polynomial `p(x) = (3x^3 – 10x^2 – 27x + 10)` and verify the relation between its zeroes and coefficients.
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.




If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
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
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`21/8, 5/16`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
