Question

If A and B are the zeroes of polynomial x² +bx +c. Find a polynomial whose zeroes are A½ and B½

Answer 1

Answer:

x²- x√ ( -b+2√c) +√c

Step-by-step explanation:

let p(x)=x² +bx +c

A and B are the zeroes of p(x)

so A+B=-b  AB=c

===========

let z=√A +√B

z²=(√A +√B)²=A+B+2√AB

z²=-b+2√c

hence z=√A +√B=√ ( -b+2√c)

polynomial whose zeroes are √A and √B

say g(x)=x²-(√A +√B)x+√AB

g(x)=x²- x√ ( -b+2√c) +√c

Answer 2

Answer:

x²- x√ ( -b+2√c) +√c

let p(x)=x² +bx +c

A and B are the zeroes of p(x)

so A+B=-b  AB=c

===========

let z=√A +√B

z²=(√A +√B)²=A+B+2√AB

z²=-b+2√c

hence z=√A +√B=√ ( -b+2√c)

polynomial whose zeroes are √A and √B

say g(x)=x²-(√A +√B)x+√AB

g(x)=x²- x√ ( -b+2√c) +√c

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Step-by-step explanation: