If one of the zeroes of the quadratic polynomial (k - 1) x2 + kx + 1 is - 3, then the value of k is
A quadratic polynomial, whose zeros are - 3 and 4, is
If the zeros of the quadratic polynomial x2 + (a + 1)x + b are 2 and - 3,
Then
The number of polynomials having zeroes as - 2 and 5 is
If one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is - 1, then the product of the other two zeroes is
The zeroes of the quadratic polynomial x2 + 99x + 127 are
The zeroes of the quadratic polynomial x2 + kx + k where k≠0,
If the zeroes of the quadratic polynomial ax2 + bx + c, where c≠0, are equal, then
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it
Which of the following is not the graph of a quadratic polynomial?
Can x2 - 1 be the quotient on division of x6 + 2x3 + x - 1 by a polynomial in x of degree 5?
What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p≠0?
If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degree of p (x) and g(x)?
If on division of a non - zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degree of p (x) and g (x)?
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Are the following statements ‘true’ or ‘False’? Justify your answer.
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
If the graph of a polynomial intersects the x - axis at only one point it need not be a quadratic polynomial.
If the graph of a polynomial intersects the x - axis at exactly two points, it need not be a quadratic polynomial.
If two of the zeroes of cubic polynomials are zero then it does not have linear and constant terms.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
If all three zeroes of a cubic polynomial x3 + qx2 - bx + c are positive, then at least one of a, b and c is non - negative.
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeroes is 1/2
4x2 - 3x - 1.
3x2 + 4x - 4.
5t2 + 12t + 7.
t3 - 2t2 - 15t.
2x2 + 7/2 x + 3/4.
4x2 + 52x - 3.
2s2 - (1 + 22)s + 2.
v2 + 43v - 15.
.
7y2 - 11y/3 - 2/3.
For each of 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 factorization.
- 23, - 9
If the zeroes of the cubic polynomial x3 - 6x2 + 10 are of the form a, a + b and a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
If √2 is zero of the cubic polynomial 6x3 + 2x2 - 10x - 42, the find it’s other two zeroes.
Find k, so that x2 + 2x + k is a factor of 2x4 + x3 - 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials.
If x - 5 is a factor of the cubic polynomial x3 - 35x2 + 13x - 35, then find all the zeroes of the polynomial.
For which values of a and b, the zeroes of q (x) = x3 + 2x2 + a are also the zeros of the polynomial p(x) = x5 - x4 - 4x3 + 3x + b? Which zeroes of p(x) are not the zeroes of p (x)?
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