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If two zeroes of the polynomial x^4+x^3-15x^2-29x-6 and 2+_√5 find other zeroes

Posted by Divyanshi Rathore ❣ 5 years, 3 months ago

CBSE > Class 10 > Mathematics

2 answers

Aastha Barbate 5 years, 3 months ago

Two zeroes of given equation are x=2+√5 & x=2-√5=0 x-2-√5=0 & x-2+√5=0 Both are the factors of the given poly. =[(x-2)-(√5)]×[(x-2)+(√5)] = (x-2)^2 - (√5)^2 [ Since (a+b)(a-b)=a^2-b^2] = x^2 - 4x + 4 - 5 = x^2 - 4x - 1 = 0 ...(1) Dividing the given poly. By eq. (1), we get, x^4 + x^3 - 15x^2 - 29x -6 ---------------------------------- x^2 -4x - 1 =x^2 +5x + 6=0 Above equation is another factor of given equation By solving it, =x^2 + 3x + 2x + 6 = 0 =x(x + 3) + 2(x +3) = 0 =(x+3) (x+2) = 0 x+3=0 & x+2=0 x=-3 & x= -2 x = -3,-2 are another's zeroes of the given poly.

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Aastha Barbate 5 years, 3 months ago

Given equation.x^4 + x^3 - 15x^2 - 29x - 6

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Posted by Kanika . 5 days, 19 hours ago

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