math

Question

0

799

2

+96

1)

If the polynomial x^2+bx+c has exactly one real root and b=c+1, find the value of the product of all possible values of c.

2)

The quadratic x^2-3x+1 can be written in the form (x+b)^2+c, where b and c are constants. What is b+c?

daddypig Feb 9, 2020

edited by daddypig Feb 9, 2020

noobfromvn26 · Answer 1 · 2020-02-09T09:04:30

"the polynomial x^2+bx+c has exactly one real root" => Discriminant : b^2 - 4*a*c = 0

but a = 1 => b^2-4c = 0 (1)

we also have : b = c+1 (2)

Solve for the set of equation of (1) and (2) => c = 1.

noobfromvn26 · Answer 2 · 2020-02-09T09:08:42

About q2:

x^2 - 3x + 1 = x^2 - 2 * (3/2) * x + (9/4) - (9/4) + 1 = (x - 3/2)^2 - 5/4.

=> b = -3/2 ; c = -5/4