Question

from a quadratic polynomial whose zeros are 7+2 root 2 and 7-2 root 2

Answer 1

Hope this helps u my friend

Answer 2

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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