In NCERT 10th math, determine whether numbers are composite by factoring them into a product of two numbers greater than one, and recall the definitions of prime and composite numbers.

Demonstrate a contradiction-based proof that three plus two root five cannot be rational, using algebraic manipulation and the relationship with root five to show inconsistency.

Presents a contradiction-based proof that one or two is an iteration in limbo, by assuming a counterexample and deriving inconsistency.

Determine whether the decimal expansion terminates or repeats by analyzing the denominator. Analyze the caption's concept of non terminating repeating expansion to guide problem solving.

Learn how decimal expansions terminate only when the denominator has the form 2^a 5^b, otherwise they are non-terminating repeating decimals.

solve the quadratic by factoring to find its zeros, then verify the relation between zeros and coefficients: the sum of roots equals -b/a and the product equals c/a.

Identify the zeros of the quadratic, showing roots ±√15, and verify that the sum and product of zeros match the coefficients: sum equals -b/a and product equals c/a.

Apply Vieta's formulas to relate the sum and product of zeros to a quadratic polynomial. Choose convenient coefficients, such as a=3, b=-3, c=1, to obtain 3x^2 - 3x + 1, illustrating multiple valid quadratics.

Apply long division to test if p squared minus three is a factor of the given polynomial. A zero remainder confirms divisibility and reveals the quotient.

the lecture demonstrates polynomial division by long division, identifying the dividend, divisor, and quotient, and shows a zero remainder with the dividend equaling the divisor times the quotient.

The lecture defines x as the cost of one apple and y as the cost of one grape, derives two equations 2x+y=160 and 2x+y=150, and shows algebraic and graphical representations.

Compare the ratios of coefficients for two linear equations to determine whether they intersect at a point, are coincident, or are parallel, indicating unique, infinite, or no solution.

Compare the ratios of coefficients in two linear equations to decide if the lines intersect at a point, are coincident, or are parallel, yielding unique, infinite, or no solutions.

Compare ratios of coefficients in two linear equations to determine consistency or inconsistency. Identify cases of intersecting, coincident, and parallel lines, and illustrate unique, infinite, or no solutions.

Use the substitution method to solve two linear equations for supplementary angles, where x+y=180 and the larger angle exceeds the smaller by 18 degrees, yielding 99 and 81 degrees.