Question

x^2-2x-8=0 find zeros
​

Answer 1

Answer:

Step-by-step explanation:

Given : Quadratic polynomial x²-2x-8=0

To find : The zeros of the quadratic polynomial relationship between zeroes and coefficients ?

Solution :

First we solve the quadratic polynomial to get the roots of the polynomial.

Applying Middle term split,

x²-2x-8=0

=>x²-4x+2x-8=0

=>x(x-4)+2(x-4)=0

=>(x-4)=0,(x+2)=0

=>x=4,x= -2

So, The roots of the quadratic polynomial are ∝=4,β= -2

The zeros of the polynomial are

∝+β=4-2=2

The zeros of the quadratic polynomial relationship between zeroes and coefficients is

Let a is the coefficient of x², b is the coefficient of x and c is the constant

i.e. Substituting, a=1,b=-2 and c=-8

Sum of zeros is

∝+β= -b/a

=>∝+β= -(-2/1)

=>∝+β=2

It is verified.

Product of zeros is

∝β=c/a

=>∝β= -8/1

=>∝β= -8

It is verified.