Find the smallest values of p for which the quadratic equation x² - 2(p + 1)x+p² = 0 has real roots

Find the smallest value of p for which the quadratic equation x²-2(p+1)x+p²=0 has real roots. Find .

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the

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If cot theta + cos theta = p and cot theta - cos theta = q, prove that p ^ 2 - q ^ 2 = 4sqrt(pq)

Find the values of p for which quadratic equation given as (p+4) x^2-(p+1)x+1=0 has real and equal

Find the smallest value of p for which the quadratic equation x2−2(p+1)x+p2=0 has real roots. Hence,

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If sum of first m terms of an A.P. is the same as the sum of its n terms,then show that the sum its

The sum of the first three terms of an AP is 33. If the product of the first and the third term exce

CBSE 2025 MAINS// Find the smallest value of p for which the quadratic equation x^2 −2(p+1)x+p^2 =0

In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ = 15° and

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A train travels at a certain average speed for a distance of 63km and then travels a distance of 72k

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A horse, a cow, and a goat are tied, each by ropes of length 14m, at the corners A, B, and C respect

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