Quadratic equations & discriminant
Practice Flashcards
How do you solve a quadratic by factorising?
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All Flashcards in Topic 2.7
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2.7.19 cards
How do you solve a quadratic by factorising?
Set it to = 0, write as two brackets, then set each bracket to zero.
State the quadratic formula.
x = (−b ± √(b² − 4ac)) / (2a), for ax² + bx + c = 0.
Before factorising or using the formula, what must you do?
Rearrange the equation so one side is 0.
How do you solve (x − h)² = n?
Square-root both sides with ±: x − h = ±√n, then solve.
Why keep the ± when rooting?
A square has two roots; dropping ± loses a solution.
Which method always works for any quadratic?
The quadratic formula.
When should you use the GDC to solve?
On Paper 2 — use the equation solver or read the x-intercepts.
Solve x² − 5x + 6 = 0.
(x − 2)(x − 3) = 0 ⇒ x = 2 or 3.
How do you read a, b, c for the formula?
From ax² + bx + c = 0 (set to zero first); keep their signs.
2.7.29 cards
What is the discriminant?
Δ = b² − 4ac — the expression under the root in the quadratic formula.
What does Δ > 0 mean?
Two distinct real roots; the graph cuts the x-axis twice.
What does Δ = 0 mean?
One repeated real root; the graph touches the x-axis (tangent).
What does Δ < 0 mean?
No real roots; the graph misses the x-axis.
How do you set up a tangency problem?
Set line = curve, form a quadratic = 0, then set Δ = 0 (one intersection).
'Equal roots' translates to which condition?
Δ = 0.
'No real roots' translates to which condition?
Δ < 0.
x² + kx + 9 = 0 has equal roots. Find k > 0.
Δ = k² − 36 = 0 ⇒ k = 6.
Do you need to solve the quadratic to count its roots?
No — just compute Δ and read its sign.
2.7.39 cards
First step to solve a quadratic inequality?
Rearrange to one side, then find the roots (solve = 0).
Upward parabola: where is f(x) < 0?
Between the roots.
Upward parabola: where is f(x) > 0?
Outside the roots: x < p or x > q.
Downward parabola: where is f(x) > 0?
Between the roots (the reverse of an upward one).
How do you write the 'outside' solution?
Two inequalities joined by 'or': x < p or x > q.
How do you write the 'between' solution?
A single chain: p ≤ x ≤ q (or p < x < q).
Open vs closed ends?
Use ≤/≥ (closed) when equality is included; </> (open) when not.
If you multiply an inequality by a negative, what happens?
Reverse the inequality sign.
Solve x² − x − 6 > 0.
Roots −2, 3; upward → outside: x < −2 or x > 3.
Topic 2.7 study notes
Full notes & explanations for Quadratic equations & discriminant
Math AA SL exam skills
Paper structures, command terms & tips
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