Question

find the zeros of quadratic polynomial 3X²-2 verify the relations between zeros and coefficient

Answer 1

$\sqrt{ {3}^{2} } {x}^{2} - \sqrt{ {2}^{2} }$
a^2-b^2= (a+b)(a-b)
$( \sqrt{3} x - \sqrt{2} )( \sqrt{3} x + \sqrt{2} )$
2 zeroes are
$\frac{ \sqrt{2} }{ \sqrt{3} }$
and
$- \frac{ \sqrt{2} }{ \sqrt{3} }$
verification =sum of zeroes = -b/a
$\frac{ \sqrt{2} }{ \sqrt{3} } - \frac{ \sqrt{2} }{ \sqrt{3} } = \frac{0}{3}$
0=0
product of zereos=c/a
-root 2/root3× root 2 /root3 = ca
-2/3=-2/3

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Answer 2

Answer:

3x^2-2 is the given quadratic polynomial

To get zeroes of the polynomial we should equate to 'zero 0'

3x^2-2=0

3x^2=2

x^2=2/3

x=root of (2/3) (OR) -root of(2/3)

VERIFICATION :-

The relatin between zeroes and coefficients is

(i) Sum of zeroes=-(coefficient of x)/(coefficient of x^2)

Root (2/3)-root (2/3)=-0/3

0=0

(ii) Product of zeroes = constant / (coefficient of x^2)

Root of(2/3)×-root of(2/3)=-2/3

-[root of (2/3)]^2=-2/3

-2/3=-2/3

Hence verified

HOPE IT HELPS!!