Question

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

Answer 1

x² - 2√3x - 4

Step-by-step explanation:

Question :-

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

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Solution :-

Roots = √3 + √7 & √3 - √7

Sum of roots = √3 + √7 + √3 - √7

=> √3 + √3 + √7 - √7

=> 2√3

Product of roots = (√3 + √7)(√3 - √7)

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

=> 3 - 7

=> - 4

Quadratic equation = x² -(sum of roots)x + (product of roots)

=> x² -(2√3)x + (-4)

=> x² - 2√3x - 4

So,

the quadratic equation = x² - 2√3 - 4.

hope it helps.