Solution of Chapter 2. Polynomials (NCERT - Exemplar Mathematics Book)

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.

Are the following statements ‘true’ or ‘False’? Justify your answer.

If the graph of a polynomial intersects the x - axis at only one point it need not be a quadratic polynomial.

Are the following statements ‘true’ or ‘False’? Justify your answer.

If the graph of a polynomial intersects the x - axis at exactly two points, it need not be a quadratic polynomial.

Are the following statements ‘true’ or ‘False’? Justify your answer.

If two of the zeroes of cubic polynomials are zero then it does not have linear and constant terms.

Are the following statements ‘true’ or ‘False’? Justify your answer.

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.

Are the following statements ‘true’ or ‘False’? Justify your answer.

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.

Are the following statements ‘true’ or ‘False’? Justify your answer.

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.

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.

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

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.

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)?