Question

find a quadratic polynomial whose zeroes are 5+ root 3 and 5 - root 3​

Answer 1

GIVEN:

• Zeroes = 5 + √3 , 5 - √3

TO FIND:

• Find a quadratic polynomial ?

SOLUTION:

Let

• $\alpha$ = 5 + √3
• $\beta$ = 5 – √3

We have to find the sum of Zeroes:

• Sum of Zeroes = 5 + √3 + 5 –√3
• Sum of Zeroes = 10

And, the product of Zeroes are:-

• Product of Zeroes = (5 + √3)(5 – √3)
• Product of Zeroes = 25 –5√3 + 5√3 –3
• Product of Zeroes = 22

We know that, the formation of a quadratic polynomial is:-

$\large{\boxed{\bf{\star \: POLYNOMIAL = x^2 -sx + p \: \star}}}$

Where,

• s = Sum of Zeroes
• p = Product of Zeroes

According to question:-

On putting the given values in the formula, we get

$\rm{\hookrightarrow x^2 -(10)x + 22 }$

$\bf{\hookrightarrow x^2 -10x + 22}$

❝ Hence, the quadratic polynomial is x² –10x + 22 ❞

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Answer 2

Answer:

$\huge\bold\star\red{Answer}$

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Given:-

• zeroes of a polynomial which are (5+√3) and (5-√3)

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To find:-

• the polynomial

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Solution:-

• If we are given zeroes of a polynomial,we have to use the given formula to find the polynomial

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Required formula:-

${x}^{2} - (sum \: of \: zeroes) + product \: of \: zeroes$

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Now,

sum of zeroes=(5+√3)+(5-√3)

=10

product of zeroes=(5+√3)(5-√3)

=5^2-(√3)^2

=25-3

=22

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Putting the value of sum and product of zeroes,we get

${x}^{2} - 10x + 22$

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hence,the required polynomial is

${x}^{2} - 10x + 22$

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$\huge\green{Hope\:this\:help\:you}$