Question

obtain all the zeroes of the polynomial x4+5x3-6x2-32x+32 if two zeroes are 1 and -4​

Answer 1

I think...

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This is a incorrect question..

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Plz check it again..

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♪＼(*＾▽＾*)／＼(*＾▽＾*)／

Answer 2

Given :-

x⁴ + 5x³ - 6x² - 32x + 32

To Find :-

Other two zeroes

Solution :-

Since highest power is 4. So, It will have two more zeroes

x = 1

x - 1 = 0

x = -4

x - (-4) = 0

x + 4 = 0

Now

Multiply both

(x - 1)(x + 4)

(x × x) + (4 × x) - (1 × x) - (1 × 4)

x² + 4x - x - 4

x² + 3x - 4

Divide x⁴ + 5x³ - 6x² - 32x + 32/x² + 3x - 4

=  x² + 2x - 8

Now

x² + (4x - 2x) - 8

x² + 4x - 2x - 8

x(x + 4) - 2(x + 4)

(x - 2)(x + 4)

Either

x - 2 = 0

x = 0 + 2

x = 2

or

x + 4 = 0

x = 0 - 4

x = -4