Write the quadratic equation whose roots are -6 and 6, and whose leading coefficient is 1 .

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23-06-2020
Mathematics

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Write the quadratic equation whose roots are -6 and 6, and whose leading coefficient is 1 .

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mberisso mberisso · Answer 1 · 2020-06-23T23:09:21+02:00

Answer:

The quadratic equation is: [tex]y=x^2-36[/tex]

Step-by-step explanation:

If the roots of the quadratic equation are "-6" and "6", then it must have the following factors: [tex](x+6)\,\, and \,\,(x-6)[/tex]

Therefore, we can write the equation in factor form as:

[tex]y=a\,(x+6)\,(x-6)[/tex]

where a is a real number constant factor. Now, this equation in standard form will look like:

[tex]y=a\,(x^2+6x-6x-6^2)=a\,(x^2-36)=ax^2-36\,a[/tex]

Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant factor [tex]a[/tex] must be "1". The final expression for the quadratic becomes:

[tex]y=x^2-36[/tex]