Question

which of the number 1,-1 and - 3 are zeros of the plolynomial 2x4 +9x3 +11x2 +4x-6​

Answer 1

Answer:

-3 is the zero of this polynomial.

Answer 2

Step-by-step explanation:

$2 {x}^{4} + 9 {x}^{3} + 11 {x}^{2} + 4x - 6 = 0 \\ \\ 2 {x}^{4} + 4 {x}^{3} + 4 {x}^{2} + 5 {x}^{3} + 10 {x}^{2} + 10x - 3 {x}^{2} - 6x - 6 = 0 \\ \\ 2 {x}^{2} ( {x}^{2} + 2x + 2) + 5x( {x}^{2} + 2x + 2) - 3( {x}^{2} + 2x + 2) = 0 \\ \\ ( {x}^{2} + 2x + 2)(2 {x}^{2} + 5x - 3) = 0 \\ \\ ( {x}^{2} + 2x + 2)(2 {x}^{2} + 6x - x - 3) = 0 \\ \\ ( {x}^{2} + 2x + 2)(2x(x + 3) - 1(x + 3)) = 0 \\ \\ ( {x}^{2} + 2x + 2)(2x - 1)(x + 3) = 0 \\ \\ {x}^{2} + 2x + 2 = 0 \\ \\ no \: real \: x \\ \\ 2x - 1 = 0 \\ \\ x = \frac{1}{2} \\ \\ x + 3 = 0 \\ \\ x = - 3 \\ \\ therefore \: the \: real \: roots \: of \: the \: polynomial \: are \\ \\ \frac{1}{2} \: and \: \: - 3$

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