Question

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

(Use the letter x to represent the variable.)

Answer 1

Answer: (x-3)(x-5) = x2 - 8x + 15

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

Explanation:

Answer 2

y = 3x² + 6x - 45

Explanation:

given roots x = a and x = b then the factors are (x - a) and (x - b)

then the quadratic is the product of its factors

y = a(x - a)(x - b) ← a is a multiplier

here x = - 5 and x = 3 with a = 3 , then factors are

(x - (- 5)) and (x - 3) , that is (x + 5) and (x - 3) , then

y = 3(x - 3)(x + 5) ← expand factors using FOIL

y = 3(x² + 2x - 15) ← distribute parenthesis by 3

y = 3x² + 6x - 45