Question

Write the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 3.

(Use the letter to represent the variable)

Answer 1

Quadratic equation form is ax ^2 + bx  +c  = 0

Required quadratic equation roots are 4 and 5,

Then the factors are (x  - 4) and (x  - 5).

But the leding coefficient is 3.

So x ^2 coefficient is 3.

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

(3x  - 12)(x  - 5) = 0

3x ^2 - 15x - 12x + 60 = 0

3x ^2 - 27x + 60 = 0

The equation is 3x ^2 - 27x + 60 = 0.