Quadratic polynomial

Degree 2 means the highest power of x is 2. So x² - 4 and 2x² - 3x - 9 are quadratic polynomials, but 3x + 1 is not. The graph of a quadratic polynomial is a curve called a parabola. It opens upwards when a is positive and downwards when a is negative.

A quadratic polynomial has at most two zeroes. They are tied to the numbers a, b and c. The chapter calls this the relationship between zeroes and coefficients.

A small example

Split 2x² - 3x - 9 into factors: 2x² - 3x - 9 = (2x + 3)(x - 3). Each factor gives a zero, so x = 3 and x = -3/2. The parabola cuts the x-axis at these two points. It opens upwards, because a = 2 is positive.

Where marks go

Question 23 of CBSE's 2025-26 Maths Basic sample paper gives the zeroes of x² + (a + 1)x + b as 2 and -3. It asks for a and b, for 2 marks. The board's Maths Basic marking scheme for 2025-26 splits the 2 marks into two 1-mark steps. Its working uses the sum of the zeroes to find a = 0, and the product to find b = -6.

Here the sign matters. The sum of the zeroes is minus the coefficient of x, divided by the coefficient of x². So 2 + (-3) = -(a + 1), which gives a = 0. Each rule used is a mark, in the way step marking works.

About the author

Mohit Sardana

Chief Architect

An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.

Mohit Sardana on LinkedIn