Question

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

(Use the letter to represent the variable.)

Answer 1

The quadratic equation with roots 5 and 1 and a leading coefficient of 5 is 5x^2 - 30x + 25 = 0.

Step-by-step explanation:

To write a quadratic equation with roots 5 and 1, and a leading coefficient of 5, we use the fact that if α and β are roots of a quadratic equation, then the equation can be written as a(x - α)(x - β) = 0, where a is the leading coefficient. Here, our roots (α and β) are 5 and 1, respectively, and our leading coefficient (a) is 5. Thus, our equation is 5(x - 5)(x - 1) = 0. Expanding this, we get 5(x2 - 6x + 5) = 0, which simplifies to 5x2 - 30x + 25 = 0.

Answer 2

Answer: the equation is

5x^2 -30x - 25

Step-by-step explanation:

A quadratic equation is one in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where c is a constant and a is the leading coefficient

Assuming we want to write the quadratic equation in x, from the information given, the given roots are 5 and 1 and the leading coefficient is 5. We will just multiply the expression by the leading coefficient.

Therefore, the linear factors of the quadratic will be (x-5) and (x-1)

With the leading coefficient as 5, the equation becomes

5(x-5)(x-1)

= 5(x^2 - x - 5x + 5)

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

= 5x^2 -30x - 25