Question

Find the relation ship between zeroes and coefficient of x^2+7x+12

Answer 1

Hi ,

Let p( x ) = x² + 7x + 12

compare p( x ) with ax² + bx + c ,


a = 1 , b = 7 , c = 12

i ) sum of the zeroes = - b/a = -7/1 ---( 1 )

ii ) product of the zeroes = c/a = 12/1 ---( 2 )

p( x ) = x² + 7x + 12

To find the zeroes of p ( x ) , we have to

take p( x ) = 0

x² + 7x + 12 = 0

x² + 4x + 3x + 12 = 0

x( x + 4 ) + 3(x + 4 ) = 0

( x + 4 )( x + 3 ) = 0

x + 4 = 0 or x + 3 = 0

x = -4 or x = -3

Therefore ,

sum of the zeroes = -4 -3 = -7---( 3 )

product of the zeroes = ( -4 )( -3 ) = 12 --( 4 )

( 1 ) = ( 3 )

( 2 ) = ( 4 )

I hope this helps you.

: )