Question

it two zeroes of the polynomial x⁴+x³-15x²-29x-6 and 2±(√5). Find other zeroes. ​​

Answer 1

Answer:

Given two of roots are 2+\sqrt{5}

5

and 2-\sqrt{5}

5

Let other two roots be X,Y

Sum of roots of above equation=-b/a

2+\sqrt{5}2+

5

+2-\sqrt{5}2−

5

+X+Y=-1/1

4+X+Y=-1

X+Y=-5

and also Product of roots=e/a

(2+\sqrt{5}2+

5

)*(2-\sqrt{5}2−

5

)*X*Y= -6

-1*X*Y=-6

X*Y=6 and X+Y=-5

X*(-5-X)=6

-5X-X^2=6

X^2+5X+6=0

X=-2 and X=-3

So Y=-2 and Y=-2

So other two roots are -2 and -3

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Answer 2

Answer:

$As  are the zeroes of p(x), so  are the factors of p(x).</p><p></p><p></p><p></p><p>Dividing p(x) by x 2 – 4x + 1</p><p></p><p></p><p></p><p></p><p></p><p>Hence, other two zeroes of p(x) are – 5 and 7.</p><p></p><p>$

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