Finding a Quadratic Function Find a quadratic function

Ormezzani6cuu

Ormezzani6cuu

Answered question

2022-04-07

Finding a Quadratic Function Find a quadratic function f (with integer coefficients) that has the givenzeros. Assume that b is a positive integer and a is an integer not equal to zero.
(a) ±b()i
(b) a±bi

Answer & Explanation

slaastro132z

slaastro132z

Beginner2022-04-08Added 8 answers

Step 1
To determine:
Find a Quadratic function f (with integer coefficients) that has the given zeroes. Assume that b is a positive integer and a is an integer not equal to zero.
(a) ±b()i
(b) a±bi
Step 2: Calculation
Part a)
Consider x=±b()i be the zeroes of the quadratic function.
Since, x=b()i is the zero of the quadratic function, therefore, (xb()i) is a factor of quadratic function.
Also, since, xb()i is the zero of the quadratic function, therefore, (x+b()i) is a factor of quadratic function.
So, the quadratic function is given by:
(xb()i)(x+b()i)
=(x2(b()i)2)[(ab)(a+b)]
=x2b(i)2
=x2b(1)[i2=1]
=x2+b
madking711kzcb

madking711kzcb

Beginner2022-04-09Added 9 answers

Part b)
Consider x=a±bi be the zeroes of the quadratic function.
Since, x=a+bi is the zero of the quadratic function, therefore, (x(a+bi)) is a factor of quadratic function.
Since, x=abi is the zero of the quadratic function, therefore, (x(abi)) is a factor of quadratic function.
So, the quadratic function is given by:
(x(a+bi))(x(abi))
=((xa)bi)((xa)+bi)
=((xa)2(bi)2)[(ab)(a+b)]
=x2+a22axb2(i)2
=x2+a22axb2(1)[i2=1]
=x22ax+a2+b2

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