+355 What is the sum of the squares of the roots of \(18x^2 +21x - 400\)?
+1443 Let's find the sum of the squares of the roots of the expression: 18x2+21x−400
We can find the sum of the squares of the roots of a quadratic expression by factoring the expression and using the fact that the sum of the squares of the roots is equal to the coefficient of the quadratic term (the x2 term) plus twice the product of the linear term's coefficient (the x term) and the constant term.
Steps to solve: 1. Factor the expression: 18x2+21x−400
We can factor the expression using the sum-product pattern and extracting common factors.
2. Find the sum of the squares of the roots: Once we have the factored expression, we can identify the coefficient of the quadratic term and the product of the linear term's coefficient and the constant term.
Solution: Following the steps above, we get the factored expression: (6x−25)(3x+16)
The coefficient of the quadratic term is 18 and the product of the linear term's coefficient and the constant term is (−21)(−400)=8400.
Therefore, the sum of the squares of the roots is: 18+2(8400)=16818
Answer: The sum of the squares of the roots of the expression is 16818.
