if alpha and beta are the zeroes of the polynomial p(x) = x²-x-4 find the value of 1/ alpha + 1/ beta + alpha × beta
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if alpha and beta are the zeroes of the polynomial p(x) = x²-x-4 find the value of 1/ alpha + 1/ beta + alpha × beta
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Answer:
-17/4
Step-by-step explanation:
Let P(x)=0
x^2-x-4=0
Here, the sum of roots= alpha+ beta=-b/a= --1/1= 1
The product of roots=alpha*beta= c/a= -4/1= -4
therefore 1/alpha+1/beta+alpha*beta is (alpha+beta)/alpha*beta+ alpha*beta
Which is ((alpha+ beta)+(alpha*beta)^2)/alpha*beta
Therefore ((1)+(-4)^2)/-4
17/-4
Which is -17/4
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