Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Find the quotient and the remainder when:
f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 + 1 – x.
It is given in the question that,
f (x) = x4 – 3x2 + 4x + 5
And, g (x) = x2 + 1 – x
Hence,
Quotient q (x) = x2 + x - 3
Remainder r (x) = 8
Verify that 3, ‒2, 1 are the zeros of the cubic polynomial p(x) = x3 – 2x2 – 5x + 6 and verify the relation between its zeros and coefficients.
Verify that 5, –2 and are the zeros of the cubic polynomial p(x) = 3x3 - 10x2– 27x + 10 and verify the relation between its zeros and coefficients
Find a cubic polynomial whose zeros are 2, –3 and 4
Find a cubic polynomial whose zeros are , 1 and –3.
Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, –2 and –24 respectively.
f(x) = x3 – 3x2 + 5x –3 is divided by g(x) = x2 – 2.
f(x) = x4 – 5x + 6 is divided by g(x) = 2 – x2.
By actual division, show that x3 – 3 is a factor 2x4 + 3x3 – 2x2 – 9x – 12.
On dividing 3x3 + x2 + 2x + 5 by a polynomial g(X), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
Verify division algorithm for the polynomials f(x) = 8 + 20x + x2 ‒ 6x3 and g(x) = 2 + 5x ‒ 3x2.
It is given that ‒1 is one of the zeros of the polynomial x3 + 2x2 ‒ 11x ‒ 12. Find all the zeros of the given polynomial.
If 1 and ‒2 are two zeros of the polynomial (x3 ‒ 4x2 ‒ 7x + 10), find its third zero.
If 3 and ‒3 are two zeros of the polynomial (x4 + x3 ‒ 11x2 ‒ 9x + 18), find all the zeros of the given polynomial.
If 2 and ‒2 are two zeros of the polynomial (X4 + x3 ‒ 34x2 ‒ 4x + 120), find all the zeros of the given polynomial.
Find all the zeros of (x4 + x3 ‒ 23x2 ‒ 3x + 60), if it is given that two of its zeros are √3 and ‒√3.
Find all the zeros of (2x4 ‒ 3x3 ‒ 5x2 + 9x ‒ 3), it being given that two of its zeros are √3 and – √3.
Obtain all other zeros of (x4 + 4x3 ‒ 2x2 ‒ 20x ‒15) if two of its zeros are √5 and – √5.
Find all the zeros of the polynomial (2x4 ‒ 11x3 + 7x2 + 13x ‒ 7), it being given that two of its zeros are (3 + √3) and (3 ‒ √3)