# Number Systems Question 7 || 9&10 Math Capsule || Misbah Sir || Infinity Learn Class 9&10 | Summary and Q&A

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June 8, 2023
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Infinity Learn NEET
Number Systems Question 7 || 9&10 Math Capsule || Misbah Sir || Infinity Learn Class 9&10

## TL;DR

The minimum value of a given quadratic expression is 192, achieved when certain variables are equal to 0.

## Key Insights

• ❎ The given quadratic polynomial is simplified using the completing the square method.
• 😑 The minimum value of the quadratic expression occurs when certain variables are equal to 0.
• 😑 The minimum value of the expression is 192, achieved by setting a - 3B and C - 3 to 0.

## Transcript

so we have been given with a quadratic polynomial over here of which we have to find the smallest value so you see over here this is 3A Square 27 b square and minus 18 A B so can I take 3 is common out of these three things over here if you use suppose x minus y the whole Square identity over here I'm going to get a minus 3B the whole Square over h... Read More

### Q: How is the given quadratic polynomial simplified using the completing the square method?

The completing the square method involves factoring out common factors and manipulating the expression to achieve a perfect square form. In this case, the polynomial is grouped and simplified by factoring out common factors.

### Q: What is the significance of the minimum value in this context?

The minimum value indicates the lowest possible value that the quadratic expression can attain. It is achieved when specific variables are set to 0, resulting in a minimum output for the expression.

### Q: Can you explain the concept of the square identity used in simplifying the expression?

The square identity involves adding and subtracting a certain value from an expression to complete a perfect square form. By manipulating the expression and using the square identity, the quadratic polynomial can be simplified further.

### Q: How is the minimum value of the expression determined?

The minimum value occurs when certain variables in the expression are equal to 0. In this case, setting a - 3B and C - 3 to 0 results in the minimum value of 192 for the quadratic expression.

## Summary & Key Takeaways

• The given quadratic polynomial is simplified using the completing the square method.

• By factoring out common factors and applying the square identity, the expression is reduced to a simplified form.

• The minimum value of the expression occurs when certain variables are equal to 0, resulting in a minimum value of 192.