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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively (i) $\frac{1}{4}, -1$ (ii) $\sqrt{2}, \frac{1}{4}$ (iii) $0, \sqrt{5}$ (iv) $1, 1$ (v) $- \frac{1}{4}, \frac{1}{4}$ (iv) $4, 1$

Asked on 2024-06-01 04:43:00 by Somu | Votes 0

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients (i) $x^2 – 2x – 8$ (ii) $4s^2 – 4s + 1$ (iii) $6x^2 – 3 – 7x$ (iv) $4u^2 + 8u$ (v) $t^2 – 15$ (vi) $3x^2 – x – 4$

Asked on 2024-06-01 04:39:50 by Somu | Votes 1

The graphs of $y = p(x)$ are given in Fig. below, for some polynomials $p(x)$. Find the number of zeroes of $p(x)$, in each case

Asked on 2024-06-01 04:36:25 by Somu | Votes 1

Prove that $3 + 2 \sqrt{5}$ is irrational

Asked on 2024-06-01 04:24:42 by Somu | Votes 0

Prove that $\sqrt{5}$ is irrational

Asked on 2024-06-01 04:23:09 by Somu | Votes 1

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Asked on 2024-05-31 12:19:20 by Somu | Votes 0

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Asked on 2024-05-31 12:18:55 by Somu | Votes 0

Check whether 6n can end with the digit 0 for any natural number n.

Asked on 2024-05-31 12:18:44 by Somu | Votes 0

Given that HCF (306, 657) = 9, find LCM (306, 657)

Asked on 2024-05-31 12:18:32 by Somu | Votes 0

Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25

Asked on 2024-05-31 12:18:14 by Somu | Votes 28

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Asked on 2024-05-31 12:17:51 by Somu | Votes 30

Express each number as a product of its prime factors: 140, 156, 3825, 5005, 7429

Asked on 2024-05-31 12:17:15 by Somu | Votes 3

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