Relation Between Roots and Coefficients
If a and b are the roots of ax2 + bx + c = 0 then a + b = -b/a and a*b = c/a.
What is Relation Between Roots and Coefficients?
If a and b are the roots of ax2 + bx + c = 0 then a + b = -b/a and a*b = c/a.
Key formula / rule: a2 + b2 = (a + b)2 - 2ab.
Key points
- Compute symmetric functions of roots from the coefficients.
- Construct a quadratic equation whose roots satisfy a stated transformation.
Common exam trap
Dropping the leading coefficient and writing the sum of roots as -b.
Definitions
- Term
Relation Between Roots and Coefficients
- Meaning
If a and b are the roots of ax2 + bx + c = 0 then a + b = -b/a and a*b = c/a.
- Term
Relation Between Roots and Coefficients — explanation
- Meaning
These relations let symmetric functions of the roots be evaluated without finding the roots at all. Every expression symmetric in the roots can be rewritten in terms of the sum and the product.
Learning objectives
Compute symmetric functions of roots from the coefficients.
Construct a quadratic equation whose roots satisfy a stated transformation.
Formulae
- Key point
a2 + b2 = (a + b)2 - 2ab.
- Key point
The quadratic with given sum s and product p is x2 - sx + p = 0.
- Key point
The relations extend to higher degrees as Vieta's formulae.
Prerequisites
MAT-U1-CQ-T2-S1-C1
Common mistakes
Dropping the leading coefficient and writing the sum of roots as -b.
Using the relations on an equation that has not been written in standard form.
Keywords
Relation
Between
Roots
Coefficients
Practice preview
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