Question

write the quadratic equation whose roots are 3 and 1, and whose leading coefficient is 4. (use the letter x to represent the variable.) \\(\square = 0\\)

Explanation:

Step1: Use root form of quadratic

If roots are $r_1$ and $r_2$, the equation is $a(x-r_1)(x-r_2)=0$, where $a$ is leading coefficient. Here $a=4$, $r_1=3$, $r_2=1$.
$4(x-3)(x-1)=0$

Step2: Expand $(x-3)(x-1)$

Multiply the binomials: $(x-3)(x-1)=x^2 - x - 3x + 3 = x^2 - 4x + 3$

Step3: Multiply by leading coefficient

Multiply the expanded polynomial by 4: $4(x^2 - 4x + 3) = 4x^2 - 16x + 12$

Answer:

$4x^2 - 16x + 12 = 0$