Find the value a for which polynomial x2 + 10x3 + 25x2+15x +a is exactly divisible by x+7.
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If a and ß are two zeroes of the quadratic polynomial p(x) =2x2-3x+7,find :-
a) 1/a + 1/ß b) a2+ß2
If the sum of the squares of zeroes of the polynomial 6x2+x+k is 25/36, find the value of k?
If p and q are the zeroes of polynomial ax2-5ax x c-+, find the values of a and c,
if p+q = pq=10
Find the zeroes of quadratic x2-2x-8 and verify the relationship between the zeroes and
their co-efficient
Find a quadratic polynomial with sum of zeroes = 1/4 and product of zeroes 1/4.
7 Write the zeroes of the polynomial x– x – 6.
Find the zeros of the quadratic polynomial 6x2 – 7x – 3 and verify the relationship
between the zeros and the coefficients.
If the ratios of the polynomial ax3+3bx2+3cx+d are in AP, Prove that 2b3- 3abc+a2 d=0
If a and ß are the zeros of a Quadratic polynomial such that a + ß2 = 24, a - ß = 8.
Find a Quadratic polynomial having a and ß as its zeros.
Find the value for K for which x2 + 10x3 + 25x2 + 15x + K exactly divisible by x + 7
If the squared difference of the zeros of the quadratic polynomial x2 + px + 45 is
equal to 144 , find the value of p.
On dividing the polynomial 4x4 - 5x3 - 39x2 - 46x – 2 by the polynomial g(x)
the quotient is x2 - 3x – 5 and the remainder is -5x + 8.Find the polynomial g(x).
If a,ß are the zeros of the polynomial 2x2 – 4x + 5 find the value of
a) a2 + ß
b) (a - ß)2
If the polynomial is divided by another polynomial, the remainder comes out to be x + a, find k and a.
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If two zeroes of the polynomial are, find other zeroes.
If the zeroes of polynomial are, find a and b.
Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
On dividing by a polynomial g(x), the quotient and remainder were x - 2 and - 2x + 4, respectively. Find g(x).
Obtain all other zeroes of , if two of its zeroes are .
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, - 14 respectively.
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
(i)
(ii)
(iii)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes ofp(x), in each case.
(iv)
(v)