Question

Are the following statements true or false? Justify your answer.
1— If the zeroes of a quadratic polynomial ax2 + bx + c are positive, then a, b and c all have the same sign
2— if the graph of a polynomial intersects three x axis at only one point, it cannot be a quadratic polynomial
3— if the graph of a polynomial intersects the x axis at exactly two points, or need not to be a quadratic polynomial
4— if two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant term

Answer 1

Answer:

1.YES

2.YES

3.NO

4.true

Step-by-step explanation:

2.Yes it can be a quadratic polynomial because quadratic polynomials have atmost two zeroes but not exactly two zeroes. When the graph line of a polynomial intersects x axis at only one point, then it says that the polynomial has two equal roots(where discriminant=0)

3.If the graph of a polynomial intersects the x – axis at only one point, then it cannot be a quadratic polynomial because a quadratic polynomial may touch the x-axis at exactly one point or intersects x-axis at exactly two points or do not touch the x-axis.

4.Let the general cubic polynomial be ax3+bx2+cx+d=0. ... Since two zeroes of the cubic polynomial are zero then the equation will be ax3+bx2=0, this does not have linear term (coefficient of x is 0) and constant term.