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

Question

slaastro132z · Accepted Answer

Step 1To 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±biStep 2: CalculationPart a)Consider x=±b()i be the zeroes of the quadratic function.Since, x=b()i is the zero of the quadratic function, therefore, (x−b()i) is a factor of quadratic function.Also, since, x−b()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:(x−b()i)(x+b()i)=(x2−(b()i)2)[∵(a−b)(a+b)]=x2−b(i)2=x2−b(−1)[∵i2=−1]=x2+b

madking711kzcb · Accepted Answer

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=a−bi is the zero of the quadratic function, therefore, (x−(a−bi)) is a factor of quadratic function.So, the quadratic function is given by:(x−(a+bi))(x−(a−bi))=((x−a)−bi)((x−a)+bi)=((x−a)2−(bi)2)[∵(a−b)(a+b)]=x2+a2−2ax−b2(i)2=x2+a2−2ax−b2(−1)[∵i2=−1]=x2−2ax+a2+b2

Finding a Quadratic Function Find a quadratic function

Answered question

Answer & Explanation

New Questions in Algebra I