Question

find the zeros of a polynomial 7x²-x-6. and verify its relationship with the coefficient.

Answer 1

Solution :

Given p(x) = 7x²-x-6

Let p(x) = 0

=> 7x²-x-6 = 0

=> 7x² - 7x + 6x - 6 = 0

=> 7x( x - 1 ) + 6( x - 1 ) = 0

=> ( x - 1 )( 7x + 6 ) = 0

=> x - 1 = 0 or 7x + 6 = 0

=> x = 1 or x = -6/7

Therefore ,

1 , -6/7 are two zeroes of p(x).

Verification :

Compare p(x) with ax²+bx+c, we get

a = 7 , b = -1 , c = -6

i ) Sum of the zeroes = 1 - 6/7

= ( 7 - 6 )/7

= 1/7

= - b/a

ii ) Product of the zeroes = 1 × ( -6/7 )

= -6/7

= c/a

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