Try factorising first. For x² + 5x + 6 find two numbers that multiply to 6 and add to 5: 2 and 3, so (x + 2)(x + 3) = 0.
If no neat pair appears after a minute, move on to the formula. It always works.
Quadratic expressions: factorising or the formula, which should I use?
Science forumMathematics
DADISI Mathematics Team
2 hours ago · 316 views
Solving x² + 5x + 6 = 0 by factorising was quick, but for 2x² + 3x − 7 = 0 I could not find factors. When should I use the formula?
Notes: /subjects/mathematics/topics/357-quadratic-expressions
Notes: /subjects/mathematics/topics/357-quadratic-expressions
13 replies
What is the formula again?
x = [−b ± √(b² − 4ac)] ÷ 2a for ax² + bx + c = 0.
What does the part under the square root tell us?
That is the discriminant. If it is positive there are two real roots, zero gives one repeated root, and negative gives none.
For 2x² + 3x − 7 = 0, a = 2, b = 3 and c = −7?
Yes. b² − 4ac = 9 + 56 = 65, so x = (−3 ± √65) ÷ 4, which is about 1.27 or −2.77.
Do I need a calculator for that?
For NECTA you may leave the surds as √65 if the question does not ask for decimals.
Is completing the square also needed?
Yes, it is in the syllabus. It also shows where the formula comes from.
Practise with a real paper: /papers/view/647
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