Write the quadratic equation whose roots are 3 and 5, and whose leading coefficient is 3.

Question

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Answer 1

The roots are x = 3 and x = 5 and the leading coefficient is 3, so the equation is:

3 * (x - 3) * (x - 5)

= 3 * (x² - 5*x - 3*x + 15)

= 3 * (x² - 8*x + 15)

= 3x² - 24x + 45

Answer 2

(x-3)(x-5) = x² - 8x + 15

 

The roots will be unchanged by multiplication by 3: 3x² - 24x + 45

Answer 3

If the roots are 3 and 5, your factors are x - 3 and x - 5.  Multiply those, then multiply the whole thing by 3.

 

3(x - 3)(x - 5) = your answer

 

Don't forget to combine like terms.