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

If graph of quadratic polynomial ax ^(2)+bx+c cuts positive 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.

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

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

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

If one of the zeroes of a quadratic polynomial of the form x^2 + ax + b is the negative of the other, then it

The graph of a quadratic polynomial y= ax^2+ bx +c (a, b, c in R) with vertex on yaxis is as shownin the figure. Then which one of the following statement is CORRECT?(A) Product the roots the corresponding quadratic equation is positive.Aof of(B) Discriminant of the quadratic equation is negative.(C) Nothing can be the sum of the roots, whether positive, negative or zero.definite said about(D) Both roots of the quadratic equation are purely imaginary.

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

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) .