Question

Write the quadratic equation whose roots are 5 and -3, and whose leading coefficient is 1

Answer 1

1. A quadratic equation has the following form: ax²+bx+c.

2. The leading coefficient is the number that is attached to the variable with the highest exponent. Then, the "a" is the leading coefficient of the quadratic equation.

3. The problem says that the leading coefficient is 1 (a=1) and the roots of the quadratic equation are 5 and -3. Then, you have:

(x-5)(x+3)=0

4. When you apply the distributive property, you obtain:

x²+3x-5x-15=0
x²-2x-15=0

5. Therefore, the answer is:

x²-2x-15=0