Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients 6x²-3-7x​

Answer 1

First of all factorise : $\sf 6x^2 - 7x-3$

$\sf = 6x^2 - ( 9 - 2 )x - 3$

$\sf = 6x^2 - 9x + 2x - 3$

$\sf = 3x(2x - 3) + 1 (2x - 3)$

$\sf = ( 3x + 1 )( 2x - 3 )$

FOR FINDING ZEROES :

• 3x + 1 = 0 ; 3x = -1 ; x = -1/3
• 2x - 3 = 0 ; 2x = 3 ; x = 3/2

Now,

VERIFICATION :

Here,

a = 6 ; b = - 7 ; c = - 3

■ Sum of zeroes = b/a

=> -1/3 + 3/2 = 7/6

=> 7/6 = 7/6

•°• L.H.S = R.H.S

■ Product of zeroes = c/a

=> -1/3 × 3/2 = -3/6

=> -3/6 = -3/6

•°• L.H.S = R.H.S

Hence proved!

$\rule{200}2$