" In a cubic polynomial "p(x)=x^(3)+ax^(2)+bx+c," sum of the zeroes "=

Mention the following with respect to the cubic polynomial ax^(3) + bx^(2) + cx + d (a) Sum of the zeroes (b) Sum of the product of the zeroes, taken two at a time .

If one zero of a quadratic polynomial p(x) =ax^(2)+bx+c is square of the other, then give the relation in a, b and c.

The condition on the polynomial p(x)= ax^(2) + bx +c, a ne 0 , so that its zeroes are reciprocal of each other, is

Are the following statements 'True' or 'False'? Justify your answer. (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. (ii) If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial. (iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not ve a quadratic polynomial. (iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms. (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. (vi) If all three zeroes of a cubic polynomial x^(3) +ax^(2) - bx +c are positive, then atleast one of a,b and c is non-negative. (vii) The only value of k for which the quadratic polynomial kx^(2) +x +k has equal zeroes is (1)/(2) .

Are the following statements True or False Justify your answers. 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 .

Verify that 1, 2 and (3)/(2) are the zeroes of the cubic polynomial p(x)= 2x^(3)-9x^(2)+13x-6 . Then, verify the relationship between the zeroes and the coefficient of the polynomial.

If one of the zeroes of the cubic polynomial x^(3)+ax^(2)+bx+c is -1 ,then find the product of other two zeroes.

If one of the zeroes of the cubic polynomial x^(3)+ax^(2)+bx+c is -1, then the perpendicular of the other two zeroes is

If one of the zeroes of the cubic polynomial x^(3)+ax^(2)+bx+c is -1, then the product of the other two zeroes is

If one of the zereos of the cubic polynomial x^(3)+ax^(2)+bx+c is -1, then the product of the other two zeroes is