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Exercise 2.5 - 10th Class Math | Waqas Nasir

Waqas Nasir・79 minutes read

Quadratic equations with specific roots are solved by calculating the sum and product of roots to find the equation using a specific formula provided in the text. The process involves determining the values of alpha and beta, finding the sum and product of the roots, and using them to calculate the quadratic equation.

Insights

Quadratic equations involve finding roots through formulas or factorization, with the sum and product of roots being crucial in determining the equation.
The process of finding quadratic equations with specific roots requires calculating the sum and product of roots, then applying these values to the formula x - sum of roots + product of roots = 0 to derive the equation accurately.

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Recent questions

How are quadratic equations defined?
Quadratic equations have a maximum variable power of two.
How can roots of quadratic equations be determined?
Roots of quadratic equations can be found by solving using formulas or factorization.
What is the formula to find roots of a quadratic equation?
The formula to find roots is x - sum of roots + product of roots = 0.
How can the quadratic equation be determined using sum and product of roots?
By substituting the sum and product of roots into the formula, the quadratic equation can be found.
What are the steps involved in finding the quadratic equation with given roots?
The process involves writing a statement, calculating the sum and product of roots, and then applying the formula to find the quadratic equation.

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Summary

00:00

"Writing Quadratic Equations with Specific Roots"

Exercise 2.5 from the 10th class will be solved, with a wallpaper showing question timings.
The question focuses on writing quadratic equations with specific roots.
Quadratic equations have a maximum variable power of two.
Roots of quadratic equations can be found by solving using formulas or factorization.
The formula to find roots is x - sum of roots + product of roots = 0.
Sum of roots is the addition of the given roots, while product of roots is their multiplication.
The quadratic equation can be determined using the sum and product of roots.
The formula for the quadratic equation is x - sum of roots + product of roots = 0.
By substituting the sum and product of roots into the formula, the quadratic equation can be found.
The process involves writing a statement, calculating the sum and product of roots, and then applying the formula to find the quadratic equation.

13:11

Finding Roots of Quadratic Equations: Sum & Product

The variables x, s, and p represent the sum and product of roots in a quadratic equation.
If the sum of roots is represented by s and the product by p, the equation x + s = p is formed.
The roots of a quadratic equation can be found by solving for x in the equation x + s - p = 0.
The roots of a quadratic equation with sum of -2 and 3 are -2 and 3.
To find the roots of a quadratic equation, the sum and product of the roots need to be determined.
The sum of roots of a quadratic equation with roots 0 and -3 is -3, while the product is 0.
The quadratic equation with roots 2 and -6 has a sum of -4 and a product of 12.
The roots of a quadratic equation with sum of -8 and product of -1 are -7 and -1.
The quadratic equation with roots 3 + √2 and 3 - √2 has a sum of 6 and a product of 7.
To find the roots of an equation given its roots, a new equation must be formulated based on the given roots.

25:39

"Roots Formula: Sum and Product Calculation"

The text discusses a formula involving roots, specifically x s - sx3 = 0.
The formula requires finding the values of alpha and beta, which are the roots of the equation.
The text explains that the equation cannot be solved directly without knowing the values of alpha and beta.
To calculate alpha and beta, the sum and product of the roots need to be determined.
The sum of the roots is found by adding alpha and beta, which is equal to -b/a.
The product of the roots is calculated by multiplying alpha and beta, which is equal to c/ba.
The text provides examples of calculating the sum and product of the roots using specific values.
Once the sum and product of the roots are known, they can be used to form the equation x s - sx3 = 0.
The text emphasizes the importance of finding the numerical values of the sum and product of the roots.
The process involves understanding the formula, determining the values of alpha and beta, and using them to calculate the equation with the given roots.

39:21

"Finding Roots and Sum in Quadratic Equations"

The equation requires four roots to find the sum of the roots.
The statement needs to be rewritten to repeat the process.
The roots are alpha square and beta square.
Equate alpha s + b s to solve the equation.
Adding alpha beta will complete the square.
The sum of the roots is -3, with a product of 6.
The roots are alpha and beta.
The product of the roots is 6.
The required quadratic equation is x s + 3x + 36 = 0.
The sum of the roots is 3, with a product of 6.

52:04

Roots and Products of Quadratic Equations

To convert to square, use the formula Squa-2 of alpha + b hole equals Beta.
The product of the roots is represented by alpha beta.
The sum of the roots is 3 and the product of the roots is 6.
The required quadratic equation is x s - sx-f = 0, with sum of the roots as -1/2 and product of the roots as 6.
The roots of the equation x s - 3x + 6 = 0 are alpha and beta.
The sum of the roots is 7/2 and the product of the roots is 3/2.
The required quadratic equation is x 2x s + x + 2 = 0.
The roots of the equation are alpha and beta, with sum of the roots as 7/2 and product of the roots as 3/2.
The equation with roots alpha and beta is px2 = 0, with sum of the roots as -p and product of the roots as p.
The sum of the roots is -p and the product of the roots is p.

01:05:13

Roots, Sum, Product, Equations: Key Formulas Explained

The equation c divided by a is constant if c is constant.
If q is present, q multiplied by a equals 1.
The product Off the Roots is obtained when Dino Minette does not write.
The roots of the Required Equations are alpha square and beta square.
The sum of the roots of the equation is -p.
The formula for the sum of the roots is -p s - 2q.
The product of the roots is q.
The equation is x s - s equals 0, with the sum of the roots being p s - 2q.
Multiplying q on both sides of the equation results in the final equation.

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