from a quadratic polynomial whose zeros are 7+2 root 2 and 7-2 root 2
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Concept
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0
Given
Roots of the polynomial are 7+2√2 and 7-2√2
Find
Form the quadratic equation
Solution
Method 1
Let the zeroes of the quadratic equation be a and b
a = 7 + 2√ 2
b = 7 – 2√ 2
Calculating a+b and ab
a+b = 14
ab = (7+2√2)(7-2√2)
ab = 49 – 8
ab = 41
We know that
Quadratic equation = x² – (a+b)x + ab
= x² – 14x + 41
Method 2
We know that
Quadratic equation = (x-a)(x-b) = 0
= (x – 7+2√2)(x – (7-2√2))
= x² – (7-2√2)x –(7+2√2)x + (7+2√2) (7-2√2)
= x² -14x + 41
The quadratic equation with roots 7+2√2 and 7-2√2 is x²-14x + 41
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