Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$5x^2-4-8x$

Answer 1

Rearrange the follwing polynomial so as to make it in the form $a{x}^2+b+c$

$5x^2-8x-4$ ..............(1)

Product=-20

Sum =-8

Now, it becomes $5x^2-10x+2x-4$

Splitting the middle term we hav done here,

5x(x-2 ) 2(x-2 )

The factors are : 5x+2 and x-2

Zeroes are : x = -2/5 and x=2

Th relationship between the zeroes of the polynomial is as follows:

α + β= -b /a Now substitute the values n u get 8 /5

α* β = c/a Substitue th value n u get -4/5

Where a=5 , b=-8 , c=-4