Higher only · the quadratic formula
Will not factorise?
Use the quadratic
formula.
it works on
every quadratic
when the question says “to 3 s.f.” —
Formula
answers to 3 significant figures
means it will not factorise
step 1 of 4
The formula
1. Copy the formula down carefully.
2. The whole top is divided by 2a.
✓ ± means two answers
ax² + bx + c = 0
x = −b ± √b² − 4ac2a
step 2 of 4
Find a, b and c
1. It must equal 0 before you start.
2. a goes with x², b with x, c is the number.
✓ The sign belongs to the number
2x² + 3x − 4 = 0
a = 2
b = 3
c = −4 keep the sign
step 3 of 4
Substitute
1. Brackets around the negative.
2. −4 × 2 × (−4) = +32, so 9 + 32 = 41.
✓ Under the root is 41, not −23
x = −3 ± √3² − 4 × 2 × (−4)2 × 2
x = −3 ± √9 + 324
x = −3 ± √414
step 4 of 4
Two answers
1. Once with +, once with −.
2. Type the whole top in brackets, then ÷ 4.
✓ Both to 3 significant figures
x = −3 + √414 = 0.851
x = −3 − √414 = −2.35
x = 0.851 or −2.35
the quadratic formula —
= 0 first
then read off a, b, c
Brackets
around every negative
“Give your answers to 3 s.f.”
is the clue to use it.
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