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Polynomials

Are the following statement ‘True’ or ‘False’? Justify your answer.

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

Polynomials

Are the following statement ‘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.

Polynomials

Can the quadratic polynomial x² + kx + k have equal zeroes for some odd integer k > 1?

Polynomials

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 degrees of p (x) and g (x)?

Polynomials

If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x)?

Polynomials

What will the quotient and remainder be on division of ax² + bx + c by px³ + qx² + rx + s, p ≠ 0?

Polynomials

Can x² – 1 be the quotient on division of x⁶ + 2x³ + x – 1 by a polynomial in x of degree 5?

Polynomials

Can x – 1 be the remainder on division of a polynomial p (x) by 2x + 3? Justify your answer.

Polynomials

Which of the following is not the graph of a quadratic polynomial?

(A) (B)

(C) (D)

Polynomials

If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.

(B) has no linear term and the constant term is positive.

(C) can have a linear term but the constant term is negative.

(D) can have a linear term but the constant term is positive.