Question

question no.5


find a quadratic polynomial whose zeroes are (5 minus 3 root 2) and( 5 + 3 root 2)​

Answer 1

$\huge \bold{hello \: there}$

Given:

5-3√2 and 5+3√2 are the zeroes of a quadratic polynomial

We know that,

Sum of the zeroes=-b/a

Now,

5-3√2+5+3√2=-b/a

➡10=-b/a-------(1)

Also, product of the zeroes=c/a

(5-3√2)(5+3√2)=c/a

We have an identity:

(a+b)(a-b)=a²-b²

(5)²-(3√2)²=25-18

➡7=c/a----------(2)

from equations (1) and (2), we get

a=1, b=-10, c=7

So the quadratic equation will be:

x²-10x+7=0