Question

A quadratic equation whose roots are 3+2√5 and 3_2√5 is???

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x^2 - 6x - 11

Step-by-step explanation:

Method 1

Quadratic equation whose roots are 3+2√5 and 3-2√5 is

[x-(3+2√5)][x-(3-2√5)]

=x^2 - (3-2√5)x -(3+2√5)x + (3+2√5)(3-2√5)

x^2 - 3x + 2√5x - 3x - 2√5x + 9 - 20

= x^2 - 6x - 11

Method 2

Sum of the roots = 3+2√5+3-2√5

=6

Product of roots = (3+2√5)(3-2√5)

=9-20

= -11

So quadratic polynomial is

x^2 - (sum)x + product

=x^2 - 6x - 11