Zero of a quadratic expression — lesson. Mathematics State Board, Class 10.

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If the value of the polynomial

$p(x)$ at

$x = k$ is zero

$p(k) = 0$ , then the real number

$k$ is called the zero of the polynomial

$p(x)$ .

Important!

To find the zeroes of a quadratic polynomial, put

$p(x) = 0$ .

Example:

1. Find the zeroes of the quadratic expression

$p(x) = 2x^2 + 3x + 1$ .

Solution:

$p(x) = 2x^2 + 3x + 1$

Put

$p(x) = 0$ .

$2x^2 + 3x + 1 = 0$

$2x^2 + 2x + x + 1 = 0$

$2x(x + 1) + 1(x + 1) = 0$

$(2x + 1) (x + 1) = 0$

$2x + 1 = 0$ or

$x + 1 = 0$

$x = \frac{-1}{2}$ or

$x = -1$

Thus, the zeroes of

$p(x) = 2x^2 + 3x + 1$ are

$\frac{-1}{2}$ and

$-1$ .

2. Check

$2$ is a zero of the polynomial

$p(x) = 3x^2 - 5x - 2$ .

Solution:

$p(x) = 3x^2 - 5x - 2$

Put

$x = 2$ in

$p(x)$ .

$p(2) = 3(2)^2 - 5(2) - 2$

$= 3(4) - 10 - 2$

$= 12 - 12$

$= 0$

Thus,

$2$ is a zero of the polynomial

$p(x) = 3x^2 - 5x - 2$ .

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2. Zero of a quadratic expression

Theory: