Question

find the quadratic equation whose roots are 3+√7 and 3-√7​

Answer 1

X² - 6X + 2

Step-by-step explanation:

QUESTION :-

Find the quadratic equation whose roots are 3 + √7 and 3 - √7.

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SOLUTION :-

Zeroes = 3+√7 & 3-√7

Sum of zeroes = 3 + √7 + 3 - √7

=> 3 + 3 + √7 - √7

=> 6

Product of zeroes = (3 + √7)(3 - √7)

=> (3)² - (√7)²...[by the formula (a+b)(a-b) = a² - b²]

=> 9 - 7

=> 2

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Now,

using the quadratic equation formula,

=> x² -(sum of zeroes)x + (product of zeroes)

=> x² -(6)x + (2)

=> x² - 6x + 2

So,

The quadratic equation = x² - 6x + 2

hope it helps.