Suppose the side of the square piece of metal sheet be ‘x’ cm.

Then, the dimensions of the box are

9 cm × (x-18) cm × (x-18) cm

Since volume of the box is 144 cm³

9 (x-18) (x-18) = 144

(x-18)² = 16

x ² - 36x + 308 = 0

So, the side ‘x’ of the metal sheet have to satisfy the equation.

x² - 36x + 308 = 0 ..... (2)

Let us observe the L.H.S of equation (1) and (2)

Are they quadratic polynomials?

We studied quadratic polynomials of the form ax ² + bx + c, a not equal to 0 in the previous chapter.

Since, the LHS of the above equations are quadratic polynomials and the RHS is 0 they are called quadratic equations.

In this chapter we will study quadratic equations and methods to find their roots.

5.2 QUADRATIC EQUATIONS

A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a not equal to 0. For example, 2x² + x - 300 = 0 is a quadratic equation, Similarly, 2x² - 3x + 1 = 0, 4x - 3x² + 2 = 0 and 1 - x² + 300 = 0 are also quadratic equations.

In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation. That is, ax ² + bx + c = 0, a not equal to 0 is called the standard form of a quadratic equation and y = ax ² + bx + c is called a quadratic function.