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Sum and Product of the Roots (Quadratic Equations) 
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#1
Oct1209, 11:40 PM

P: 107

1. The problem statement, all variables and given/known data
For the quad equation x^2  px + 9 = 0 1. Write down the sum of roots and product of roots 2. Find p IF twice the sum of the roots EQUALS the product 3. Find p IF the roots are unequal 2. Relevant equations Sum = (a+b) = b/a Product = (ab) c/a 3. The attempt at a solution 1. Using the formula Sum = p Product = 9 2. 2p = 9 9/2 = 2p/2 = 4 1/2 3. Totally lost Can someone provide guidence. Cheers 


#2
Oct1309, 12:59 AM

Mentor
P: 21,311

Let r_{1} and r_{2} be the roots of the given quadratic.
1) Sum of roots = r_{1} + r_{2} = p Product of roots = r_{1} * r_{2} = 9 You have two equations in two unknowns. Can you solve for r_{1} and r_{2} in terms of p? 2) What's the question in this part? You have 


#3
Oct1309, 01:10 AM

P: 1,398

1 if the roots are a,b then the equation is x^2  (a+b)x + ab = 0, so the coefficient of x is (sum of the roots), and you should have p instead of p.
2. I have no idea what is meant here. 3. Find p when the roots are equal first. Can you use comples numbers? if not there are more values of p where the quadratic doesn't have a solution 


#4
Oct1309, 01:11 AM

P: 107

Sum and Product of the Roots (Quadratic Equations)
Hi there
I have edited the original question  my apologies there. Cheers 


#5
Oct1309, 01:16 AM

P: 107

I have amended my original post.
For the quad equation x^2  px + 9 = 0 1. Write down the sum of roots and product of roots 2. Find p IF twice the sum of the roots EQUALS the product 3. Find p IF the roots are unequal 2. Relevant equations Sum = (a+b) = b/a Product = (ab) c/a 3. The attempt at a solution 1. Using the formula Sum = p Product = 9 2. 2p = 9 9/2 = 2p/2 = 4 1/2 3. Totally lost Can someone provide guidence. Cheers 


#6
Oct1309, 05:05 AM

HW Helper
P: 3,540

1) No the sum is [itex]b/a=(p/1)=p[/itex] and the product is right.
2) You're right except for taking the sum as p rather than p. 3) If we need p when the roots are unequal, how about we find the value(s) of p when the roots are equal, then take all other values? 


#7
Oct1309, 08:58 PM

P: 107

I think that I have nutted out part 3, of this question
x^2  px + 9 = 0 a = 1 b = p and c = 9 Delta = b^2  4ac = (p)^2  4(1) (9) = p  36 So if plugged into the following: Equal roots Delta = 0 p  36 = 0 p = 36 For real roots Delta = >(Equal to) 0 p  36 >(Equal to) 0 Unreal Delta < 0 p  36 < 0 p < 36 For real and different Delta > 0 p  36 > 0 p > 36 Guidence on this would be great 


#8
Oct1409, 03:36 AM

HW Helper
P: 3,540

Yes you were very close. You had the right approach.
You just forgot about the squaring p in the [itex]\Delta=(p)^24.1.9[/itex] However, there were no other restrictions on the problem. It just said find p when the roots are unequal. It never said anything about the roots being real/imaginary. Basically, taking [itex]\Delta<0[/itex] is fine too. It just means for those values of p, the quadratic will be entirely above the xaxis. So finally, for roots unequal, p is all reals except [itex]p^2\neq 36[/itex] thus, [itex]p\neq \pm 6[/itex] (Note: do not forget about the plus/minus) 


#9
Oct1409, 03:44 AM

P: 107

Many thanks
I understand  many thanks for taking the time to respond so thoughtfully. Cheers 


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