Advertisements
Advertisements
प्रश्न
Find the quotient and the remainder when f(x) = x4 – 5x + 6 is divided by g(x) = 2 – x2.
Advertisements
उत्तर
f(x) as x4 + 0x3 + 0x2 – 5x + 6 and g(x) as – x2 + 2
– x2 – 2
`-x^2 + 2")"overline(x^4 + 0x^3 + 0x^2 - 5x + 6)`
x4 – 2x2
– +
2x2 – 5x + 6
2x2 – 4
– +
–5x + 10
Quotient q(x) = – x2 – 2
Remainder r(x) = –5x + 10
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 polynomials and verify the relationship between the zeroes and the coefficients
`g(x)=a(x^2+1)-x(a^2+1)`
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 p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are 2, –3 and 4.
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, –2 and –24 respectively.
Find the quotient and the remainder when f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 – x + 1.
By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
Find all the zeroes of (x4 + x3 – 23x2 – 3x + 60), if it is given that two of its zeroes are `sqrt(3)` and `-sqrt(3)`.
If α, β are the zeroes of the polynomial f(x) = x2 + x – 2, then `(α/β - α/β)`.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
A quadratic polynomial, whose zeroes are –3 and 4, is ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`7y^2 - 11/3 y - 2/3`
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
