Question

verify that 1/2,1,-2 are the zeros of the polynomial 2x3+x2-5x+2.also verif that sum of the zeros=-b/a and product of zeros =-d/a​

Answer 1

Answer:

Step-by-step explanation:

Answer:

let, f(x) = 2x³ + x² - 5x + 2

1st to verify:  are zeroes of f(x)

put

f(x) =  

    =  

    =  

    =  

    =  0

Put x = 1

f(x) = 2(1)³ + (1)² - 5(1) + 2

    = 2 + 1 - 5 + 2

    = 0

put x = -2

f(x) = 2(-2)³ + (-2)² - 5(-2) + 2

    = 2 × (-8) + 4 + 10 + 2

    = -16 +16

    = 0

Therefore,  are zeroes of given cubic polynomial.

Comparing given cubic equation with standard equation ax³ + bx² + cx + d

we get a = 2 , b = 1 , c = -5 & d = 2

Also take,

Now we verify the relation between zeroes and their coefficient,