Write the quadratic equation whose roots are 1and 4, and whose leading coefficient is 4

Question

Write the quadratic equation whose roots are  1and 4, and whose leading coefficient is 4

whpalmer4 · Answer

If we know the roots of an equation, we can write it as $$P(x) = a(x-r_1)(x-r_2)...(x-r_n)$$where the roots are $r_1,r_2,...r_n$

$a$ is a constant that can be 1 or any value required to make the curve pass through a given point, or a coefficient have a particular value.

In this case, the problem asks that the leading coefficient (that of $x^2$) be 4.  You'll need to substitute in your root values, expand the polynomial, and then solve for the value of $a$ that gives you that coefficient.

whpalmer4 · Answer

As every term of the product will involve $a$, once you find $a$ you'll need to substitute it into the product to get the final expression.