Factorize $3 x^{2} - (3 \sqrt{3} - 1) x - \sqrt{3}$ and verify relationship between the zeroes and the coefficients. [2 MARKS]

Open in App

Solution

Factorisation : 1 Mark
Verification : 1 Mark

Given polynomial is,

$3 x^{2} - (3 \sqrt{3} - 1) x - \sqrt{3}$

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

$= 3 x (x - \sqrt{3}) + 1 (x - \sqrt{3})$

$= (x - \sqrt{3}) (3 x + 1)$

So the zeroes are,

$x - \sqrt{3} = 0 \Rightarrow x = \sqrt{3}$

$3 x + 1 = 0 \Rightarrow x = - \frac{1}{3}$

For verification,

$α + β = \frac{- 1}{3} + \sqrt{3} = \frac{3 \sqrt{3} - 1}{3} = - \frac{b}{a}$

$α β = \frac{- 1}{3} \times \sqrt{3} = \frac{- 1}{\sqrt{3}} = \frac{c}{a}$

Suggest Corrections

Similar questions

Factorize $3 x^{2} - (3 \sqrt{3} - 1) x - \sqrt{3}$ and verify relationship between the zeroes and the coefficients. [2 MARKS]

Factorize $z^{2} + 3 \sqrt{3} z - 12$ and verify the relationship between zeroes and coefficient [2 MARKS]

Factorize $x^{3} + 3 x^{2} - 28 x$ and verify the relationship between the zeroes and coefficients.

2 \sqrt{2} x^{2} - 9 x + 5 \sqrt{3}

3 \sqrt{3} x^{2} - 19 x + 10 \sqrt{3}

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

$2 \sqrt{3} x^{2} - 5 x + \sqrt{3}$

Join BYJU'S Learning Program