If alpha and beta are the zeroes of 2x^2-5x+3 find the values of
(i)a^2+b^2
(ii)1/2^a+1/2^b
(iii)a/b+b/a
(Alpha-a, Beta-b)
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EXPLANATION.
- GIVEN
a and b are the zeroes of polynomial
2x^2 - 5x + 3
according to the question,
sum of zeroes of quadratic polynomial
a + b = -b / a = 5/2
products of zeroes of quadratic polynomial
ab = c / a = 3/2
1) = a^2 + b^2
( a + b) ^2 - 2ab
( 5/2 ) ^2 - 2(3/2)
25 / 4 - 3
25 - 12 / 4
13 / 4 = answer
2) = 1/2^a + 1/2^b
if base is same power should be add
( 1/2 ) ^ab
( 1/2 ) ^3/2
3) = a/b + b/a
a^2 + b^2 / ab
( a + b) ^2 - 2ab / ab
( 5/2) ^2 - 2 X 3/2 / 3/2
13/4 / 3/2
13/6 = answer
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