Everything Maths Grade 11

CHAPTER 7. SOLVINGQUADRATIC EQUATIONS 7.5

7.5 Finding an Equation When You Know its Roots

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We have mentioned before that the roots of a quadratic equationare the solutions or answers you get

from solving the quadratic equation. Working back from the answers, will take you to an equation.

Example 8: Find an equation whenroots are given

QUESTION

Find an equation with roots 13 and− 5

SOLUTION

Step 1 : Write down as the product of two brackets

The step before giving the solutions would be:

(x− 13)(x + 5) = 0

Notice that the signs inthe brackets are opposite of the given roots.

Step 2 : Remove brackets

x^2 − 8 x− 65 = 0

Of course, there wouldbe other possibilities aswell when each term on each

side of the equals sign is multiplied by a constant.

Example 9: Fraction roots

QUESTION

Find an equation with roots−^32 and 4

SOLUTION