find the polynomial. x3+ 8* 2 +15x
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Answer:
For finding zeroes of a polynomial p(x), put p(x) = 0.
Let p(x) = x 3 + 5x 2 – 9x – 45 and q(x) = x 3 + 8x 2 + 15x.
p(x) = x 3 + 5x 2 – 9x – 45 = 0
x 2 (x + 5) – 9(x + 5) = 0
(x + 5) (x 2 – 9) = 0
(using identity: (a 2 – b 2 ) = (a + b)(a - b))
(x + 5) (x + 3) (x – 3) = 0Now, the different values are,(x + 5) = 0, x = -5(x + 3) = 0, x = -3(x - 3) = 0, x = 3
∴ On putting p(x) = 0, we get x = -5, x = -3, x = 3 as its zeroes.