Equations and inequalities in Scientific calculator plus 991 for Android

Most of these tools never ask for the equation itself. You pick a mode for the kind of problem, the calculator lays out a grid of cells named after the coefficients, and you type the numbers; the powers of x are implied by where each number goes. This page says which tool fits which problem, and what the modes have in common.

Which tool for which problem

The last two work on the ordinary calculation screen; the rest are modes of their own.

Polynomial equations

One mode for each degree from 2 to 5. Degree 2 answers with more than its roots: after x1 and x2 it gives the x and y values of the vertex, labelled a minimum when the parabola opens upward and a maximum when it opens downward. Quadratic equations covers it. Degrees 3, 4 and 5 answer with their three, four or five roots, some of which may be equal or complex; cubic, quartic and quintic equations covers them.

Inequalities

Degrees 2, 3 and 4, with a separate mode for each relation against zero: greater than, greater than or equal, less than, less than or equal. The answer is a set, not a number, and it comes back as one: intervals such as x < −1 and 2 < x, stacked one to a line and read as "or". Polynomial inequalities explains how to read them.

Systems of equations

Two, three or four linear equations in as many unknowns, one equation to a row of the grid, with the constant from the right-hand side in the last column. The unknowns come back one at a time and are stored in X, Y, Z and T, as many as there are unknowns. Simultaneous equations takes you through it.

The Coefficient Editor

Every polynomial, inequality and system mode opens on the same thing: a grid of cells with the coefficients named across the top, one row for a polynomial and one row per equation for a system.

• Type a value and press =: the cell is evaluated and the selection moves on to the next.
• A cell takes a whole expression, a fraction or √2 as readily as a whole number. The equation and system modes accept complex numbers too.
• Enter 0 for any term the equation leaves out, so that every cell holds a value.
• ◀ left ▶ right move between cells, and ▲ up ▼ down between the rows of a system.
• AC empties every cell and puts the selection back on the first.
• Once the last cell is filled, = solves, as does the on-screen SOLVE [=] button.

Tap an answer to switch it between a fraction and a decimal.

When there is no single answer

A grid of zeros is not an equation, and the calculator says so instead of guessing. When every coefficient of x is zero but the constant is not, the equation reduces to something like 5 = 0, and a dialog reads No solution. When every coefficient is zero, it reduces to 0 = 0, which every x satisfies, and the dialog reads Infinite solution. A system says the same when its equations contradict each other or describe the same line. OK returns to the grid.

Draw it

In the polynomial and inequality modes, GRAPH plots the polynomial in the grid at any moment, while you are still typing coefficients or with an answer on screen. The roots are already marked, and in the equation modes the turning points as well. An inequality's graph also shades its solution set: a band running the full height of the graph over exactly the x values that satisfy it.

SOLVE, FACTOR, EXPAND and SIMPLY

SOLVE takes an equation from the input line, two sides joined by = (typed with ALPHA CALC =), and returns every root it finds at once, exact wherever it can, even when the answer still holds other letters. SOLVE covers it, including how to solve for a letter other than x. The three functions on the 2nd keyboard rewrite an expression rather than solve it: FACTOR turns 1 + 2x + x² into (1 + x)², EXPAND multiplies (x + y)³ out, and SIMPLY collects a·x² + b·x² into (a + b)x². Factor, expand and simplify has all six of the manual's examples.

At a glance