What is the common difference in an AP?
The common difference 'd' is the fixed value obtained by subtracting any term from the next term.
How is the sum of an AP calculated?
The sum of the first n terms is Sₙ = n/2 [2a + (n-1)d].
What is the formula for the nth term of an AP?
The formula is aₙ = a + (n - 1)d.
What is an Arithmetic Progression (AP)?
An AP is a sequence of numbers where the difference between consecutive terms is constant.
What are complex roots?
Complex roots are non-real roots that exist in pairs and are conjugates of each other (e.g., x = a + bi and x = a - bi)
How can I determine the nature of roots without solving the equation?
Calculate the discriminant Δ and use its value to identify the root type.
What do the values of the discriminant mean?
Δ > 0 : Two distinct real roots. Δ = 0 : One repeated real root. Δ < 0 : Two complex roots.
What is the discriminant?
The discriminant Δ = b²-4ac determines the nature of the roots of a quadratic equation.
What if the quadratic equation cannot be factorised?
Use other methods like the quadratic formula or completing the square.
What is the Zero Product Property?
If ab = 0, then a = 0 or b = 0.
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