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Class 10 > Learn Mathematics > If one zero of the polynomial 5z2 + 13z -- p is reciprocal...
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If one zero of the polynomial 5z2 + 13z – p is reciprocal of the other, then find p.

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Let X and 1/X be the two zeros of given polynomial Comparing given polynomial with az2+ bz +c we get a=5 b=13 c=-p Product of two zeros=-p But product of zeros =x× 1/X=1 hence p= -1
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Let x,1/x be the zeroes of the given polynomial Compare with general form ax2+bx+c now sum of the zeroes=-b/a Product of the zeroes=c/a x×1/x=-p/5 1=-p/5 p=-5
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Given 5z2 + 13z -p Let x be one zero then other zero will be 1/x as given both the zeroes are reciprocal to each other. Therefore 5x2+13x-p=0. ---------------->1 5(1/x)^2+(13/x)-p=0----------->2 Solving above equations we get p=-5
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