Question

Write a quadratic equation in the form x^2+bx+c=0x 2 +bx+c=0 that has the following roots: Roots: -10± √15

Answer 1

For this, we work backward from the Pythagorean equation.

-b±√(b2-4ac)/(2a)

We have -4±√(11)

We can determine that b = 4 and 2a=1, so a = 1/2

Next, analyze the root to find c:

√(b2-4ac) = √11

(b2-4ac) = 11, but we know a and b

(42-4(1/2)c) = 11

(16 - 2c) = 11

-2c = -5

c = 5/2

So with a = 1/2, b = 4, and c = 5/2 we have our equation

(1/2)x2 + 4x + (5/2) = 0

Explanation: