The quadratic formula

The Maths Habit
Walkthrough to print

  1. Solve x2 + 7x + 12 = 0

    x = −3 or x = −4

  2. Solve x2 − 2x − 35 = 0

    x = 7 or x = −5

  3. Solve x2 − 9x = 0

    x = 0 or x = 9

Sam says x2 = 25 has one answer, x = 5. Is Sam right?

No: (−5)2 = 25 as well

The quadratic formula

  1. a, b and cMake it = 0.
    What are a, b and c? Keep the signs.
  2. The formulaWrite the formula down.
  3. SubstitutePut the numbers in place of the letters.
  4. Work out b² − 4acWork out the part under the square root.
  5. + and −Work it out once with + and once with −.
  6. RoundGive both answers to the accuracy asked for.
ax2 + bx + c = 0
x = −b ± √b2 − 4ac2a
x = −b ± √b2 − 4 × a × c2 × a
b2 − 4ac = one number
x = −b + √number2a  or  x = −b − √number2a
x = answer 1 or x = answer 2
a minus in front makes b or c negative
a negative number goes in brackets
c negative? then the 4ac adds on
usually 2 decimal places
Walkthrough to print

What are a, b and c?

2x2 − 3x + 7 = 0 2, −3, 7

Solve x2 + 4x + 1 = 0

a =1 b =4 c =1
x =−4±√42 − 4 ×1×12 ×1
x =−0.27 or −3.73

Solve x2 + 7x + 5 = 0

a =1 b =7 c =5
x =−7±√72 − 4 ×1×52 ×1
x =−0.81 or −6.19

Solve x2 + 4x + 1 = 0

a =1 b =4 c =1
x =−4±√42 − 4 ×1×12 ×1
x =−0.27 or −3.73

Solve 2x2 + 3x − 4 = 0

a =2 b =3 c =−4
x =−3±√32 − 4 ×2×(−4)2 ×2
x =0.85 or −2.35

The quadratic formula worksheet, page 1

Answer sheet

  1. Explain why x2 + 2x + 5 = 0 has no solutions.

    b² − 4ac is negative

  2. A rectangle has sides x and x + 3. Its area is 20. Find x to 2 decimal places.

    3.22

  1. Solve x2 + 6x + 2 = 0. Give your answers to 2 decimal places.

    x = −0.35 or −5.65

  2. Solve 2x2 − 5x − 1 = 0. Give your answers to 2 decimal places.

    x = 2.69 or −0.19

  3. How many solutions does 2x2 − 3x + 2 = 0 have? Show how you know.

    None: b2 − 4ac = −7
Exit tickets to print