Question

find the zeros of 3 x square minus x minus 4 and verify the relationship between zeros and its coefficient

Answer 1

Hey.

Here is the answer.

f(x) = 3x^2 - x - 4

= 3x^2 + 3x - 4x - 4

= 3x(x + 1) -4(x + 1)

= (x + 1)(3x - 4)

For zeros (x + 1)(3x - 4) = 0

So, zeros are -1 and 4/3

Verification :

sum of zeros = -1 + 4/3 = 1/3

product of zeros = -1 × 4/3 = -4/3

and 3x^2 - x - 4 = 0

or, x^2 -1/3 x - 4/3 =0 ________ {coefficient of x^2 made 1 }

So, sum of zeros gives coefficient of x (1/3)

= - (-1/3).......as -b/a

and product of zeros gives the constant term (-4/3)

= -4/3 .........as c/a.

Thanks.

Answer 2

Heya !!!!


P(X) = 3X² - X -4



=> 3X² -4X +3X -4




=> X ( 3X -4) +1( 3X -4)





=> ( 3X-4) ( X +1) = 0



=> ( 3X -4) = 0 OR ( X +1) = 0


=> X = 4/3 OR X = -1

Let Alpha = 4/3 and beta = -1



Relationship between zeroes and Coefficient.




Sum of zeroes = Alpha + Beta = 4/3 + (-1) = 4/3 -1 = 4 - 3/3 = 1/3 = Coefficient of X/Coefficient of X².



And,



Product of zeroes = Alpha × Beta = 4/3 × -1 = -4/3 = Constant term/ Coefficient of X².




HOPE IT WILL HELP YOU...... ;-)