Question

find the zeroes of the quadratic polynomial and verify the relation between it's zeroes and co efficient x^+3x-10​

Answer 1

x²-3x-10

x² -(5x-2x)-10

x² - 5x+2x-10

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

(x-5)(x+2)

x=5

x=-2

Sum of zeroes = α+β = 5-2 = 3

α+β = -b/a = -(-3)/1 = 3

Product of zeroes = αβ = 5*-2 = -10

αβ = c/a = -10/1 = -10

Hence,proved.

Answer 2

Answer:

p(x) = x² + 3x - 10

p(x)= 0

x² + 3x - 10 = 0

x² + ( 5 -2 ) x - 10 = 0

x² + 5x - 2x - 10 = 0

x( x + 5 ) - 2 ( x + 5) = 0

( x + 5 ) ( x - 2) = 0

Therefore the zeroes are -

( x + 5 ) = 0

x = -5

and

( x - 2) = 0

x = 2

now,

sum of the zeroes = - 3/1 = -3 = -b/a = - coefficient of x / coefficient of x²

Product of the zeroes= -10/1 = -10 = c/a = constant term / coefficient of x²