Question

if one root of the polynomial 5x^3+13x+k is reciprocal of the other,then find the value of k

Answer 1

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Given:- one root of the polynomial 5x^2+13x+k is reciprocal of the other

Let to be Required Number be a

Reciprocal of a=1/a

Product of Roots=a×1/a

Sum of Zeroes=Product of Zeroes

Product of Zeroes=c/a=k/5

According to the Question statement!

Product=Required terms

k/5=1

k=5×1

k=5

Ans:- k=5

Thanks!!!

Answer 2

bonjour!

We know that in a quadratic equation ax^2 + bx + c = 0

Product of roots = c/a

Here we have the equation 5x^2 + 13x + k = 0

Product of roots = k/5

Given that the roots are reciprocals of each other. So if one root is p, the other would be 1/p. So, their product will always be 1.

=> 1 = k/5

=> k = 5.

Hence, the value of k is 5.