Checkpoint: the decider at work

The decider of x² − 7x + 9 = 0 is 49 − 36 = 13. What kind of roots does it have?

• Two irrational roots, because 13 is positive, not a square
• No real roots, because 13 is not a perfect square number
• Two rational roots, because 13 is a positive whole number

x² − 6x + 9 = 0 has decider zero. How many roots does it have?

• No roots, because the decider is not positive
• Two different roots that happen to be close together
• One value — 3 — counted twice

A classmate finds that the decider is −5. The classmate writes "the roots are irrational". What is wrong with that?

• Irrational numbers are real. A negative decider means no real root.
• The roots are rational. A negative decider always gives fractions.
• Nothing is wrong. A negative decider gives negative irrational roots.

2x² − 9x + 7 = 0 reads 81 − 56 = 25. Which method does the choosing rule pick?

• The formula at once, because a is not 1
• Factorisation — 25 is a perfect square
• Neither — the equation has no real roots

For which k does x² − 8x + k = 0 have two equal roots?

• k = 16, because 64 − 4k = 0
• k = 8, because the middle number is −8
• k = 64, because b² = 64