Question

1. Find the quadratic polynomial whose zeros are 3 and -5. 2. Express 0.5432 recurring decimals as fraction in their lowest term. 3. Given that LCM (26,169) = 338, find the HCF (26,169). 4. Find the quadratic polynomial with zeros 2 + √3 and 2 - √3. 5. If α and β are zeros of the quadratic polynomial p(x) = x2 – (k + 6)x + 2(2k – 1), then find the value of k, if α + β = (αβ)/2 6. Prove that √5 is an irrational number. 7. Show that cube of any positive integer is of the form 9m , 9m + 1 or 9m + 8 , for some integer m. 8. Find the cubic polynomial whose zeros are -2 , 3 and - 1 . 9. If the HCF of 657 and 963 is expressible in the form of 657x + 963(-17), find x.

Answer 1

1. alpha = 3

beta = -5

sum = 3+(-5)

= -2

product = 3× (-5)

= -15

polynomial = x^2 + 2x - 15

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