find a of the polynomial ax^2+(a-4)x+3 if one of the zero is the reciprocal of the other
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Given : ax²+(a-4)x+3 , one of the zero is the reciprocal of the other
To find : Value of a
Solution:
ax²+(a-4)x+3
Let say zeroes are α & 1/α
Product of Zeroes = α * 1/α = 1
Product of Zeroes = 3/a
Equating product of zeroes
3/a = 1
=> a = 3
3x² + (3 - 4)x + 3
= 3x² - x + 3
Roots are (1 ± √-35)/6
Roots are
=(1 + √35 i )/6 , (1 - √35 i )/6
a = 3
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