Question

The zeroes of the polynomial 7x^2-11x/3-
2/3 are​

Answer 1

Given :

• 7x² - 11x/3 - 2/3

To Find :

• Zeroes of the given polynomial

Soltution :

➨ 7x² - 11x/3 - 2/3 = 0

By taking LCM

➨ ( 21x² - 11x - 2 ) /3 = 0

➨ 21x² - 11x - 2 = 0

➨ 21x² - 14x + 3x - 2 = 0

➨ 7x ( 3x - 2 ) + 1 ( 3x - 2 ) = 0

➨ ( 7x + 1 ) ( 3x - 2 ) = 0

➨ 7x + 1 = 0

➨ 7x = - 1

➨ x = -1/7

➨ 3x - 2 = 0

➨3x = 2

➨ x = 3/2

Zeroes of given polynomial are -1/7 and 3/2

Answer 2

Given equation

$7x^{2} - \dfrac{11x}{3} -\dfrac{2}{3}=0$

Multiplying the equation by 3, we get,

$\implies 21x^{2} -11x-2=0$

Solving, we get,

$\implies 21x^{2} -14x+3x-2=0$

$\implies 7x(3x-2)+1(3x-2)=0$

$\implies (7x+1)(3x-2)=0$

Now,

$7x+1=0$

$\implies x = \dfrac{-1}{7}$

$3x-2=0$

$\implies x= \dfrac{2}{3}$

$\boxed{\boxed{\bold{Therefore, \ the \ zeroes \ of \ the \ polynomial \ are \ \frac{-1}{7} \ and \ \frac{2}{3} \ respectively}}}}}}$