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Algebra

Solve a quadratic equation

Find the roots of x² − 5x + 6 = 0 with a polynomial solver or the quadratic formula.

Open in Trident

A quadratic equation has the form ax² + bx + c = 0. It can have two answers, one answer or none that are real numbers.

The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. For x² − 5x + 6 = 0, the part under the root is 25 − 24 = 1, so x = (5 ± 1) / 2, which gives 3 and 2.

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Press MENU and scroll to Equation/Func (item A). Press up three times from the top of the menu to reach it, then press =.

    MENU▲▲▲=

  2. Choose 2 for Polynomial, then 2 for degree 2.

    22

  3. Type the coefficients one at a time: a = 1, b = −5, c = 6, pressing = after each.

    1=(−)5=6=

You should seex1=3 x2=2

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Press MENU and 5 for the Equation mode. Press F2 for Polynomial, then F1 for degree 2.

    MENU5F2F1

  2. Enter a = 1, b = −5, c = 6, pressing EXE after each.

    1EXE(−)5EXE6EXE

  3. Press F1 (SOLVE).

    F1

You should seex1=3 x2=2

Natural Color Graphing key reference

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Press menu, 3 (Algebra), 1 (solve). Type the equation x² − 5x + 6 = 0, then a comma and x.

    menu31xx²−5x+6=0,x)

  2. Press enter. Both roots are listed.

    enter

You should seex=2 or x=3

Classic CAS key reference

Classic Graphing 84 · Using the equation solver

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Open MATH, go up to Solver and press enter. Type X² − 5X + 6 (equal to zero) and press enter.

    math▲enterX,T,θ,nx²−5X,T,θ,n+6enter

  2. The solver finds the root closest to the guess. Type a guess of 4 and press alpha then enter. It finds 3.

    4alphaSOLVEenter

You should seeX²−5X+6=0 X=3

Try a guess of 1 to find the other root, 2.

Classic Graphing 84 key reference

RPN Advanced 42 · Quadratic formula on the stack

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Work out the part under the root: b² − 4ac = 25 − 24. Key in 5, ENTER, then use shift and the √x key for x², then subtract 24.

    5ENTER⇧x²√x24−

  2. Take the square root and store it in register 01.

    √xSTO01

  3. The larger root is (5 + root) / 2. Add 5 and divide by 2.

    5+2÷

  4. The other root is (5 − root) / 2. Key in 5, recall the root, subtract, and divide by 2.

    5RCL01−2÷

You should seey: 3.0000 x: 2.0000

RPN Advanced 42 key reference

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