Math (quadratic equation)

Question

Write the quadratic equation whose roots are −2

 and 1

, and whose leading coefficient is 3

.

Answer 1

y=(x+2)(x-1) = x^2 +x -2

3y + 3f(x) = 3x^2 +3x -6

that's a quadratic equation with leading coefficient 3 and zeroes -2 and 1

Answer 2

If the roots of the polynomial are -2 and 1, the factors of the polynomial would be:

(x+2)(x-1) which when multiplied equals x^2 + x - 2.

Since they want the first coefficient to be 3, we just multiply all the terms of the polynomial by 3: 3x^2 + 3x - 6,

which factors to (3x+6)(x-1), which would provide the same roots when equated to zero.