Question

for the polynomial p(x)=x²-3x-4 verify the relationship between the zeros and coffecient​

Answer 1

Answer:

x²-3x-4=0 .                                      

x²-4x+x-4=0

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

(x-4)(x+1)=0

x= -1 or 4

sum of roots = 4-1=3= -[-3]/1 = coefficient of x

product of roots =-4 = -4/1= constant term

henceproved

Answer 2

Given :-

x² - 3x - 4

To Find :-

Zeroes

Solution :-

x² - 3x - 4

Spilt middle term

x² - (x - 4x) - 4

x² - x + 4x - 4

x(x + 1) - 4(x + 1)

(x + 1)(x - 4)

Either

x + 1 = 0

x = 0 - 1

x = 1

Or,

x - 4 = 0

x = 0 + 4

x = 4

Let α = -1 and β = 4

On comparing the given equation ax² + bx + c

We get

a = 1

b = -3

c = -4

α + β = -b/a

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

3 = 3/1

3 = 3

αβ = c/a

-1 × 4 = -4/1

-4 = -4