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#### Monoxdifly

##### Well-known member

- Aug 6, 2015

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1. The quadratic equation whose roots are k less than the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle a(x+k)^2+b(x+k)+c=0\).

2. The quadratic equation whose roots are k more than the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle a(x-k)^2+b(x-k)+c=0\).

3. The quadratic equation whose roots are n times the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle ax+bnx+cn^2=0\).

4. The quadratic equation whose roots are negations of the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle ax^2-bx+c=0\).

5. The quadratic equation whose roots are inverses of the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle cx^2+bx+a=0\).

6. The quadratic equation whose roots are squareroots of the roots of \(\displaystyle ax^2+bx+c=0\) is \(\displaystyle a^2x^2-(b^2-2ac)+c^2=0\).

Thanks for your help.