Question

find a quadratic polynomial whose zeros are 3-√ 3\ 5 and 3 +√3\5​

Answer 1

Answer:

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Step-by-step explanation:

25x^2+30x-6

Step-by-step explanation:

the zeros are-

\alphaα --> 3-\sqrt{3}

3

/5

\betaβ --> 3+\sqrt{3}

3

/5

product of zeroes:-

\alpha \betaαβ

(3-\sqrt{3}

3

+3+\sqrt{3}

3

)/5 = 6/5

sum of zeros:-

\alpha \betaαβ

(3-\sqrt{3}

3

)/5 * (3+\sqrt{3}

3

)/5 = 9-3/25=6/25

now,

x^2-( \alpha + \betaα+β )x+( \alpha \betaαβ )=0

x^2/1-6/25+6/5*x=0

(25x^2+30x-6)/25=0

25(25x^2+30x-6)/25=0

25x^2+30x-6=0

hence , it is the quadratic polynomial