Question

Q9. Obtain all zeroes of the following polynomial, when two of its zeroes are given
a) p(x) = 2x* + x3 - 14x2 - 19x - 6, having two of its zeroes as -2 and -1.
b) p(x) = 3x* - 11x? – x2 +33x – 24, having two of its zeroes as 13 and - 13.
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Answer 1

a) 2x^4 + x^3 - 14x^2 - 19x - 6

-2,-1, ?, ?

(x+2)(x+1) =》 x^2 + (2+1)x + 2

x^2 + 3x + 2

by dividing 2x^4 + x^3 - 14x^2 - 19x - 6 by x^2 + 3x + 2

we get,

2x^2 - 5x - 3 as a quotient

2x^2 -6x + 1x -3

2x (x-3) +1 (x-3)

(x-3)(2x+1)

x = 3

x = -1/2

these are two more zeroes