Question

Find the integral zeros of the polynomial 2x^3+5x^2-5x-2

Answer 1

2x³ + 5x² - 5x - 2
= 2x³ - 2x² + 7x² - 7x + 2x - 2
= 2x²(x - 1) + 7x(x - 1) + 2(x - 1)
= (2x² + 7x + 2)(x - 1)

Here we have to factors (2x² + 7x + 2) and (x - 1)
one zero of given Polynomial , x - 1 = 0 ⇒ x = 1 ( integer )
other two zeros of given polynomial , 2x² + 7x + 2 = 0 ⇒ x = (-7 ± √33)/4 [ irrational numbers ]

Hence, internal zero of polynomial has only one e.g., x = 1

Answer 2

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