SOLUTION: form a quadratic equation in x whose roots are the squares of the roots of 2x^2-8x＋1＝0

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Question 997519: form a quadratic equation in x whose roots are the squares of the roots of 2x^2-8x＋1＝0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a quadratic equation in x whose roots are the squares of the roots of
2x%5E2-8x%2B1=0
find the roots of
2x%5E2-8x%2B1=0............use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29+
x+=+%288+%2B-+sqrt%2864-8+%29%29%2F4+
x+=+%288+%2B-+sqrt%2856+%29%29%2F4+
x+=+%288+%2B-+sqrt%284%2A14+%29%29%2F4+
x+=+%28cross%288%294+%2B-+cross%282%29sqrt%2814+%29%29%2Fcross%284%292+
x+=+%284+%2B-+sqrt%2814+%29%29%2F2+
so, exact roots are:
x+=+%284+%2B+sqrt%2814+%29%29%2F2+
x+=+%284+-+sqrt%2814+%29%29%2F2+
approximate:
x%5B1%5D+=+%284+%2B+3.741657386773941%29%2F2+=7.741657386773941%2F2=3.87
x%5B2%5D+=+%284+-+3.741657386773941%29%2F2=+0.2583426132260586%2F2=0.13

now find their squares:
x%5B1%5D%5E2+=+14.98
x%5B2%5D%5E2+=0.0169

now use zero product formula to find your equation:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-14.98%29%28x-0.0169%29
f%28x%29=x%5E2-0.0169x-14.98x-14.98%2A%28-0.0169%29
f%28x%29=x%5E2-14.9969x%2B0.253162