Question

find the zeroes of the polynomial f(x)=√3x² + 5x–8√3 and verify the relationship between the zeroes and it's coefficient​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution :-

$\sqrt{3} {x}^{2} + 5x - 8 \sqrt{3} = 0\\ by \: factorisation \: method \\ \sqrt{3} {x}^{2} + 8x - 3x - 8 \sqrt{3} = 0 \\ ( \sqrt{3} {x}^{2} + 8x)( - 3x - 8 \sqrt{3} ) = 0 \\ x( \sqrt{3}x + 8) - \sqrt{3} ( \sqrt{3} x + 8) = 0 \\ ( \sqrt{3}x + 8)(x - \sqrt{3} ) = 0 \\ \sqrt{3}x + 8 = 0 \: \: \: \: \: or \: \: \: \: \: \: x - \sqrt{3 } = 0 \\ \sqrt{3} x = - 8 \: \: \: \: \: or \: \: \: \: \: x = \sqrt{3} \\ x = \frac{ - 8}{ \sqrt{3} } \: \: \: \: \: \: or \: \: \: \: x = \sqrt{3}$

We find the factors 0f quadratic equation are 8 & -3

Let change the sign

-8, -3

Now,

Coefficient of x^2 is

$\sqrt{3}$

If we divide by Coefficient of x^2 to factors

We get the zeros are opposite number of factors

Let

$factors \: are \: 8 \: \: and \: \: - 3 \: let \: the \: change \: sign \\ - 8 \: \: \:and \: \: \: 3 \\ we \: divide \: by \: coefficient \: of \: {x}^{2} \\ \frac{ - 8}{ \sqrt{3} } \: \: \: \: and \: \frac{3}{ \sqrt{3} } = \sqrt{3}$