If alpha and beta are the zeroes of the polynomial x²+x+1 then find the value of
[tex] \frac{ 1}{ \alpha } + \frac{1}{ \beta } [/tex]
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If alpha and beta are the zeroes of the polynomial x²+x+1 then find the value of
[tex] \frac{ 1}{ \alpha } + \frac{1}{ \beta } [/tex]
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GIVEN
• α and β are the zeroes of the polynomial x²+x+1.
FORMULA
• In a quadratic polynomial such as ax²+bx+c ( standard form of quadratic polynomial) if two zeroes of this polynomial α and β then
SOLUTION
• Given polynomial = x²+x+1
• This is a quadratic polynomial
• let compare this polynomial with standard form of quadratic polynomial ax²+bx+c , we get
a = 1 , b = 1 , c = 1
• The zeroes of this polynomial are α and β.
Now
Now