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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?

 Feb 9, 2020
edited by daddypig  Feb 9, 2020
 #1
avatar+29 
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"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.

 Feb 9, 2020
 #2
avatar+29 
+2

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

 Feb 9, 2020

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