Math Question

Question

Write the quadratic equation whose roots are 4 and -5, and whose leading coefficient is 5. (Use the letter x to represent the variable.)

Answer 1

When we find the roots, we set the equation equal to zero.  We can write the equation as

 

(x - 4)(x + 5) = 0

 

 

Expanding, we obtain

 

x² + x - 20 = 0

 

 

Now the leading coefficient is 5.  This is the coefficient of the x² term, the first term.  Multiply both sides of the equation by 5.

 

5x² + 5x - 100 = 0

 

 

 

Answer 2

(x-4)(x+5)=0

x^2-4x+5x-20=0

x^2+x-20=0

5x^2+5x-100=0