If alpha and beta are zeros of f(x) = 5x2 + 5x+1 Then find value of (alpha)square + (beta) square
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Given,
f(x)=5x²+5x+1
A/Q,
we know that,
Alpha+beta= -b/a
= -(+5)/5
= -1
now,
alpha×beta=c/a
= 1/5
now,
(alpha+beta)²= alpha²+ beta²+2×alpha×beta
(-1)²=alpha² +beta² +2×1/5
1= alpha ²+beta² +2/5
1-2/5=alpha²+beta²
5-2/5=alpha²+beta²
3/5= alpha² +beta²
Hence,alpha²+ beta²=3/5.
f(x)=5x²+5x+1
A/Q,
we know that,
Alpha+beta= -b/a
= -(+5)/5
= -1
now,
alpha×beta=c/a
= 1/5
now,
(alpha+beta)²= alpha²+ beta²+2×alpha×beta
(-1)²=alpha² +beta² +2×1/5
1= alpha ²+beta² +2/5
1-2/5=alpha²+beta²
5-2/5=alpha²+beta²
3/5= alpha² +beta²
Hence,alpha²+ beta²=3/5.
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