Question

(1/a - 1/ B)
(3 marks)
11. If a and B are the zeroes of x2 + px, + q then find the value of (a/B + 2). (B/ a + 2) (3 marks)
1
id
2.
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Answer 1

ANSWER:

Find relationship between Zeroes:

Sum of Zeros = -b/a

Sum of Zeros = -p/1

Sum of Zeros = -p

Product of Zeros = c/a

Product of Zeros = q/1

Product of Zeros = q

Now, We have to find the value of (α /ß + 2)(ß/α + 2)

(α /ß + 2)(ß/α + 2)

(α + 2ß)(ß + 2α)

a(ß + 2a) + 2ß(ß + 2a)

aß + 2a² + 2ß² + 4aß

(2a² + 2ß² )+ 5aß

2(a²+ß²) + 5aß

2[(a+ß)² - 2ab ] + 5ab

2[(-p)² - 2(q) ] + 5(q)

2[(p²) - 2q ] + 5q

2[p² - 2q] + 5q

2p² - 4q + 5q

2p² + q

Therefore, Required Value of (α /ß + 2)(ß/α + 2) is 2p² + q.