Question

9.Find the zeroes of the quadratic polynomial √3x2 -8x+4√3 and verify the relationship between zeroes and its coefficient.

Answer 1

${\huge{\underline{\underline{\sf {\mathfrak{Answer}}}}}}$

${\underline{\underline{\rm {Given:}}}}$

• $p(x) = \sqrt3x^2-8x+4\sqrt3$
• $Zeroes =?$

${\underline{\underline{\rm {Finding \ zeroes:}}}}$

⠀⠀⠀$\sqrt3x^2-8x+4\sqrt3=0$

⠀⠀⠀$\sqrt3x^2 -6x - 2x + 4\sqrt3=0$

⠀⠀⠀$\sqrt3x^2 -6x -2x + 4\sqrt3 =0$

⠀⠀⠀$\sqrt3x (x - 2\sqrt3 )-2(x - 2\sqrt3 ) = 0$

⠀⠀⠀$(x - 2\sqrt3)(\sqrt3x - 2)=0$

⠀⠀⠀$x-2\sqrt3 = 0 \; \; \; \; \; \sqrt3x - 2 = 0$

$\boxed{\implies{\boxed{x = 2\sqrt3 \ or \ x = \dfrac{2}{\sqrt3}}}}$

$\underline{\underline{\rm{Verification: }}}$

⠀⠀⠀$Sum \ of \ zeroes = 2\sqrt3 + \dfrac{2}{\sqrt3}$

⠀⠀⠀$Sum \ of \ zeroes = \dfrac{8}{\sqrt3}$

$\boxed{\implies{\boxed{Sum \ of \ zeroes = \dfrac{-Coefficient \ of \ x}{Coefficient \ of x^2}}}}$

⠀⠀⠀$Product \ of zeroes = 2\sqrt3 \times \dfrac{2}{\sqrt3}$

⠀⠀⠀$Product \ of \ zeroes = 4$

$\boxed{\implies{\boxed{Product \ of \ zeroes = \dfrac{Constant \ term }{Coefficient \ of \ x^2}}}}$

Answer 2

4

Step-by-step explanation:

2+2=4

3+3=6

4+4=8

5+5=10

6+6=12