Question

Write the quadratic equation whose roots are 1 and -6, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)

Answer 1

Answer:

$f(x)=5x^2+25x-30$

Step-by-step explanation:

Quadratic Equation

If the roots of a quadratic equation are known, we can form the equation as follows:

$f(x)=a(x-x_1)(x-x_2)$

where x1 and x2 are the known roots, and a is the leading coefficient.

We are given the roots as x1=1 and x2=-6, and the leading coefficient as a=5, thus:

$f(x)=5(x-1)(x+6)$

Operating:

$f(x)=5(x^2-x+6x-6)$

Simplifying:

$f(x)=5(x^2+5x-6)$

Multiplying:

$\mathbf{f(x)=5x^2+25x-30}$