write the quadratic equation whose roots are 3 and -5, and whose leading coefficient is 4.

Question

(Use the letter x to represent the variable)

--=0

If someone could show me how to do it, I would appreciate it because I can probably learn better like this and so I can do it on my own next time.

Answer 1

The roots of the equation are the values of x where the function touches the x axis —> this is when y = 0.

The factors are the expressions (typically given in parenthesis) that = 0 when x is equal to the root values.

root = 3 means when x= 3, the factor must = 0

x - 3 = 0

our factor is (x - 3)

root = -5 means when x = -5 the factor = 0

x + 5 = 0

our factor is (x + 5)

We can FOIL these factors to get a quadratic expression

first outer inner last

(x-3)(x+5)

x * x = x^2

x * 5 = 5x

-3 * x = - 3x

-3 * 5 = -15

combine like terms 5x - 3x = 2x

equation is now x^2 + 2x - 15

Lastly, we are told that the leading coefficient is 4. Right now we have a leading coefficient of 1 (when it’s “not there” it’s 1). We need to multiply every term by 4 to keep the equation true and create the leading coefficient

4*x^2

4*2x

4* -15

Final Result

y = 4x^2 + 8x - 60

Answer 2

If 3 is a root then x - 3 is a factor.

a represents the leading coefficient

P(x) = a(x - 3)(x - (-5))

P(x) = 4(x - 3)(x + 5)

Can you multiply out and answer?