Question

Write the quadratic equation whose roots are −6 and 2 , and whose leading coefficient is 5 . (use the letter x to represent the variable.)

Answer 1

Here let the quadratic equation be ax^2 + bx + c We know that a=5 from the question. Since the roots are 6 and 2, the quadratic equation would take the form of a product like (a1x-b1)(a2x-b2). However, let's assume that a2=1 and b2=6, Since a=5, a1=5, then 5x-b1=5(x-2). Solving this shows that b1=10 So, the equation is (5x-10)(x-6)