+389 Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 2, what is b?
+118694 Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 2, what is b?
for this answer I will assume it is a typo
The y intercept is the constant so c=2
p(x)=x3+ax2+bx+cp(x)=x3+ax2+bx+2
Let the zeros be α,β,andγα+β+γ=−a1soα+β+γ3=−a3αβγ=−c1=−2The coefficients are 1, a and bsoα+β+γ3=αβγ=1+a+b−a3=−2=1+a+ba=6 −2=1+6+b−2=7+bb=−9
+118694 Dabae,
Is it meant to be bc as you have entered OR is it meant to be bx ??
+118694 Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 2, what is b?
for this answer I will assume it is a typo
The y intercept is the constant so c=2
p(x)=x3+ax2+bx+cp(x)=x3+ax2+bx+2
Let the zeros be α,β,andγα+β+γ=−a1soα+β+γ3=−a3αβγ=−c1=−2The coefficients are 1, a and bsoα+β+γ3=αβγ=1+a+b−a3=−2=1+a+ba=6 −2=1+6+b−2=7+bb=−9
