If graph of quadratic polynomial `a x^2+b x+c` cuts positive direction of y-axis, then what is the sign of `c` ?

If the graph of quadratic polynomial ax^(2)+bx+c cuts negative direction of y -axis, then what is the sign of c?

State 'T' for true and 'F' for false and select the correct option. I. If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeroes are coincident. II. If a quadratic polynomial f(x) is not factorisable into linear factors, then it has no real zero. III. If graph of quadratic polynomial ax^(2)+bx+c cuts positive direction of y-axis, then the sign of c is positive. IV. If fourth degree polynomial is divided by a quadratic polynomial, then the degree of the remainder is 2.

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) .

The graph of the quadratic polynomial y=ax^(2)+bx+c is as shown in the figure.Then

If both the zeros of the quadratic polynomial ax^2 + bx + c are equal and opposite in sign, then find the value of b.

The graph of a quadratic polynomial ax^(2)+bx+c=y(a,b,c,in R,a!=0) then the incorrect statement is

Are the following statements True or False Justify your answers. If the zeroes of a quadratic polynomial ax^(2)+bx+c are both positive ,then a ,b and c all have the same sign .

Draw the graph of the quadratic polynomial f(x)=3-2x-x^(2)

If a makes 30^@ with the positive direction of x-axis, angle beta with the positive direction of y-axis and angle gamma with the positive direction of z-axis, then what is cos^2beta+cos^2gamma eqaul to ?