Sign of a quadratic polynomial

Problems based on graphs of quadratic polynomial | Sign of quadratic polynomial | sum and products of roots and nature of roots

Result based on Sign of Quadratic Polynomial

Graphs of quadratic polynomial and their application, Problems related to sign of quadratic polynomial

Identification of sign of coefficients of quadratic polynomial based on graph

The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

The sum and product of the zeroes of a quadratic polynomial are 2 and - 15 respectively. The quadratic polynomial is

Which of the following is a quadratic polynomial ?

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 sum and product of zeroes of a quadratic polynomial are -(1)/(6) and -(1)/(3) respectively What is the quadratic polynomial.

The sum and product of the zeros of a quadratic polynomial are -(1)/(2) and -3 respectively.What is the quadratic polynomial.