Polynomials — Part 2: Zeroes and coefficients of a quadratic: visual lesson, CBSE Class 10 Mathematics (Standard 041 / Basic 241)

Lesson

Polynomials, Part 2: Zeroes and coefficients

The coefficients already know the sum and product of the zeroes.

In this lesson you will

Zeroes $2$ and $5$: sum $7$, product $10$ — read straight from the coefficients.

Concept

Diagram

Each factor $(px + q)$ gives the zero $-\dfrac qp$.
Polynomial	$ac$	Split $b$ as	Factors	Zeroes
$x^2 - 7x + 10$	$10$	$-2, -5$	$(x - 2)(x - 5)$	$2, 5$
$2x^2 + x - 6$	$-12$	$4, -3$	$(2x - 3)(x + 2)$	$\dfrac32, -2$
$10x^2 - 3x - 1$	$-10$	$-5, 2$	$(2x - 1)(5x + 1)$	$\dfrac12, -\dfrac15$

For $ax^2 + bx + c$ , find two numbers whose product is $ac$ and whose sum is $b$ . Split $bx$ with them and factorise in pairs.