Q1.Answer the following and justify:

(i) Can x

(i) Can x

^{2}– 1 be the quotient on division of x^{6}+ 2x^{3}+ x – 1 by a polynomial in x of degree 5?.**Solution: **

(ii) What will the quotient and remainder be on division of ax

^{2}+ bx + c by px^{3}+ qx^{2}+ rx + s, p ≠ 0?.**Solution: **

(iii) 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)?.

**Solution: **

(iv) 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)?.

**Solution: **

(v) Can the quadratic polynomial x

^{2}+ kx + k have equal zeroes for some odd integer k > 1?.**Solution: **

Q2. Are the following statements ‘True’ or ‘False’? Justify your answers.

(i) If the zeroes of a quadratic polynomial ax

(i) If the zeroes of a quadratic polynomial ax

^{2}+ bx + c are both positive, then a, b and c all have the same sign.**Solution: **

**Solution: **

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

**Solution: **

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

**Solution: **

(iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

**Solution: **

(v) 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.

**Solution: **

(vi) If all three zeroes of a cubic polynomial x

^{3}+ ax^{2}– bx + c are positive, then at least one of a, b and c is non-negative.**Solution: **

(vii) The only value of k for which the quadratic polynomial kx

^{2}+ x + k has equal zeros is 1/2.**Solution: **

**‹Exercise 2.1 Exercise 2.3›**

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