Given the roots 6 and 7, determine the quadratic equation?
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The roots of a quadratic equation are given as 6 and 7. This means that x - 6 = 0 and x - 7 = 0
We can write ( x - 6)( x - 7) = 0
=> x^2 - 6x - 7x + 42 = 0
=> x^2 - 13x + 42 = 0
Therefore the required quadratic equation is
x^2 - 13x + 42 = 0
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(x - 6) (x - 7)
Using FOIL, expand the equation
FOIL = First Outside Inside Last
x^2 - 7x - 6x + 42
Combine like terms
x^2-13x+42
Given the roots 6 and 7, determine the quadratic equation?
To determine the quadratic equation, we'll use Viete's relations:
x1 + x2 = S, where x1 = 6 and x2 = 7
x1 + x2 = 6+7
S = 13
x1*x2 = P
P = 6*7
P = 42
The quadratic equation is:
x^2 - Sx + P = 0
x^2 - 13x + 42 = 0
The quadratic equation is:
x^2 - 13x + 42 = 0
Another method of creating the quadratic when knowing the roots is to write the equation as a product of linear factors;
(x-x1)(x-x2) = 0
(x-6)(x-7) = 0
We'll remove the brackets:
x^2 -6x - 7x +42 = 0
We'll combine like terms and we'll get the quadratic equation:
x^2 - 13x + 42 = 0
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