Question

x^2 - (1+√3)x + √3 = 0​

Answer 1

Answer:

1 & √3

Step-by-step explanation:

=> x^2 - (1 + √3)x + √3 = 0

=> x^2 - x - √3 x + √3 = 0

=> x(x - 1) - √3(x - 1) = 0

=> (x - 1)(x - √3) = 0

Since their product is zero, one of them must be 0.

When x - 1 = 0 => x = 1

When x - √3 = 0 => x = √3

Answer 2

Required Answer:-

Given that:

• $\sf {x}^{2} - (1 + \sqrt{3} )x + \sqrt{3} = 0$

To find:

• The values of x.

Answer:

• The values of x are √3 and 1.

Solution:

$\sf {x}^{2} - (1 + \sqrt{3} )x + \sqrt{3} = 0$

$\sf \implies {x}^{2} - x - \sqrt{3}x + \sqrt{3} = 0$

$\sf \implies x(x - 1) - \sqrt{3}(x - 1)= 0$

$\sf \implies (x - \sqrt{3})(x - 1)= 0$

By zero product rule,

Either (x - √3) = 0 or (x - 1) = 0

So,

$\sf x_{1,2} = \sqrt{3} ,1$

Hence, the values of x are √3 and 1.

How to solve?

• The general form of a quadratic equation is ax² + bx + c = 0 where, a≠0 and a, b, c are real numbers. We have to split b into two real numbers x and y in such a way that x + y = b and xy = ac. Now, we will factorise by grouping method.
• Zero product rule says that if a and b are two numbers such that ab=0, then either a = 0 or b = 0 or both.
• By applying zero product rule, we can easily find out the roots.
• In this example, we can see that (x - √3)(x - 1) = 0. So, by zero product rule, either x - √3 = 0 or x - 1 = 0. In this way, we can solve this