Quadratic roots and coefficients

The roots in polynomials are closely linked to the coefficients of that polynomial.

All polynomials in this chapter will be written as follows - the letters are important here:

Sum of roots

If and are roots of , then .

This means that the sum of roots of a quadratic is equal to .

Find the sum of the roots of

• The sum of roots is :
• Answer: sum of roots =

Find the sum of the roots of

• The sum of roots is :
• Answer: sum of roots =

The sum of roots of the polynomial is 7. Find the value of .

• , ,
• The sum of roots is 7, which represents :
• Answer:

The sum of roots of the polynomial is -3. Find the value of .

• , ,
• The sum of roots is -3, which represents :
• Answer:

Product of roots

If and are roots of , then (positive).

In words, the product of roots of a quadratic is equal to .

Find the product of the roots of

• The product of roots is :
• Answer: product of roots =

Find the product of the roots of

• The product of roots is :
• Answer: product of roots =

The product of roots of the polynomial is . Find the value of .

• , ,
• The product of roots is , which represents :
• Answer:

Evaluating other expressions

The equation has roots and . Evaluate

• The only things we know about and are:
• We need to rewrite in terms of and only:
• Now we can substitute the values we know in!
• Answer:

Summary of finding roots and coefficients

	Coefficient link	Positive/Negative
Sum of roots		Negative
Product of roots		Positive