Question

Find a quadratic polynomial whose zeroes are (5+√2) and (5-√2)

Answer 1

Answer:

Let us consider the quadratic equation as :

ax2+bx+c, whose roots are αβ

We know that , α+β=−b/a

and α∗β=c/a

Here, quadratic polynomial’s zeroes means its roots

so, α=5+2–√andβ=5−2–√

now, α+β=(5+2–√)+(5−2–√)=10=−ba

and, α∗β=(5+2–√)∗(5−2–√)= 23 = c/a

52−(2–√)2=25−2=23=c/a

Therefore,

ax2+bx+c=1x2−10x+23

ANS : x2−10x+23..

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