MHB Sum and product of roots of quadratic equation

Click For Summary
The discussion focuses on deriving the sum and product of the roots of a quadratic equation using given relationships among the coefficients. The user initially finds the sum of the roots to be zero but becomes stuck in further calculations. Key equations are established, including relationships between the coefficients a, b, c, and d, leading to the conclusion that a + c equals 121. Ultimately, this results in the total sum a + b + c + d equating to 1210. The conversation emphasizes the importance of showing work to identify where confusion arises in solving quadratic equations.
Mathsonfire
Messages
11
Reaction score
0
2502444ea79b1f6544313e76b30e3cda.jpg

#85
 
Mathematics news on Phys.org
You've posted 4 questions, and I have given all 4 threads more useful titles, now I would ask that you show what you've tried in each thread. This way we can see where you're stuck.
 
Well i am stuck at this point
I found sum of zeroes in both cases and then got stuck.what should i do
 
Please post what you have so far. :)
 
We know:

$$c+d=10a$$

$$a+b=10c$$

Hence:

$$a+b+c+d=10(a+c)$$

We also know:

$$c^2-11b=a^2-11d$$

$$11d-11b=a^2-c^2$$

$$11(d-b)=(a+c)(a-c)$$

And we obtain by subtraction of the first 2 equations:

$$(d-b)-(a-c)=10(a-c)$$

Or:

$$d-b=11(a-c)$$

Hence:

$$121(a-c)=(a+c)(a-c)$$

Assuming \(a\ne c\) (otherwise \(d=b\) and the two quadratics are identical) there results:

$$a+c=121$$

Hence:

$$a+b+c+d=10\cdot121=1210$$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB How can we determine the sum of roots in a quadratic equation with real roots?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Quadratic equations intersaction point is minimum instead of roots
  • · Replies 2 ·
Replies
2
Views
1K
High School Uses for formulas for sum and product of quadratic roots
  • · Replies 9 ·
Replies
9
Views
5K
High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Quartic real roots - factor part into quadratic
  • · Replies 3 ·
Replies
3
Views
1K
MHB Expression involving roots of quadratic equation
  • · Replies 1 ·
Replies
1
Views
2K
MHB [ASK] Proof of Some Quadratic Functions
  • · Replies 6 ·
Replies
6
Views
2K
High School Can negative roots of a quadratic equation for √E be physically acceptable?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solving Quadratic Equations without CD: Better Direction?
  • · Replies 1 ·
Replies
1
Views
2K
MHB How Can You Verify the Sum of Roots in a Quadratic Equation?
  • · Replies 2 ·
Replies
2
Views
2K