Question

verify the 1 upon 2 1 - 2 are zeros of cubic polynomial 2 x cube + x square - 5 + 2​

Answer 1

Answer:

Step-by-step explanation:

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,

\alpha +\beta +\gamma =\frac{1}{2}+1+(-2)=\frac{1+2-4}{2}=\frac{-1}{2}=\frac{-b}{a}

\alpha \,.\,\beta +\beta \,.\,\gamma +\gamma \,.\,\alpha =\frac{1}{2}\times1+1\times(-2)+(-2)\times\frac{1}{2}=\frac{1}{2}-2-1=\frac{1-4-2}{2}=\frac{-5}{2}=\frac{c}{a}

\alpha\,.\,\beta \,.\,\gamma =\frac{1}{2}\times1\times(-2)=-1=\frac{-2}{2}=\frac{-d}{a}

Hence Verified

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