Question

find the zeros of quadratic polynomial and verify the relationship between the coefficient and draw the graph for the quadratic polynomial also find the nature of the route as taking its quadratic equation bracket open x square - 2 x minus 3 bracket close the 10 value is equal to x is equal to 1, 2, 3, 4 -1 -2 -3 -4​

Answer 1

(i) We have,

f(x) = x2 − 2x − 8

f(x) = x2 + 2x − 4x − 8

f(x) = x (x + 2) − 4(x + 2)

f(x) = (x + 2) (x − 4)

The zeros of f(x) are given by  

f(x) = 0

x2 − 2x − 8 = 0

(x + 2) (x − 4) = 0

x + 2 = 0

x = −2

Or

x − 4 = 0

x = 4

Thus, the zeros of f(x) = x2 − 2x − 8 are α = −2 and β = 4

Now,

x=2

Answer 2

The zeros of f(x) are given by  

f(x) = 0

x2 − 2x − 8 = 0

(x + 2) (x − 4) = 0

x + 2 = 0

x = −2