If a quadratic polynomial `f(x)` is not factorizable into linear factors, then it has no real zero. (True/false).

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.

If a quadratic polynomial f(x) is factorizable into linear distinct factors,then what is the total number of real and distinct zeros of f(x)?

If a quadratic polynomial f(x) is a square of a linear polynomial,then its two zeroes are coincident.(True/false)

Graph of quadratic polynomial When polynomial is factorable into two distinct factors

Factorize quadratic polynomial variable

A quadratic polynomial with zeroes -2 and 3, is:

A quadratic polynomial with zeroes -2 and 3, is :

Graph of quadratic polynomial when polynomial have no zeroes

The two zeroes of a quadratic polynomial 3x^(2)+1+4x are :

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) .