Question

10. The quadratic equation whose one of the root is (2+√3) and (2-√3) is
1. 2x2-4x+1=0
2. x2-4x+1=0
4. XP-6x+4=0
4. None of these


please help me​

Answer 1

Answer:

Option 2 is correct.

x² - 4x + 1 = 0

Step-by-step explanation:

We know that,

Sum of zeroes = -b/a

(2 + √3) + (2 - √3) = -b/a

2 + √3 + 2 - √3 = -b/a

4 = -b/a

b/a = -4 ------ 1

Product of zeroes = c/a

(2 + √3)(2 - √3) = c/a

Using (a + b)(a - b) = a² - b²

2² - (√3)² = c/a

4 - 3 = c/a

1 = c/a ------- 2

We know that, the Quadratic equation is of the form,

ax² + bx + c = 0

Dividing whole equation by 'a', we get

x² + (b/a)x + (c/a) = 0

From eq.1 and eq.2 we get,

x² + (-4)x + (1) = 0

x² - 4x + 1 = 0

Thus, Option 2 is correct.

Hope it helped and you understood it........All the best