Question

Find the value of k for which the roots of the equation 3x2 - 10x + k = 0 are reciprocal of each other

Answer 1

Answer:

Step-by-step explanation:

Take the roots as a&1/a

Sum of zeros is = 10/3=a+1/a

3a^2+3=10a

3a^2-10a+3

Product of zeroes=k/3=1

K=3

Answer 2

The value of k is 3.

Step-by-step explanation:

The given equation is

$3x^2-10x+k=0$

Comparing this equation the standard form ax²+bx+c=0

a = 3, b = -10, c = k

Let the zeros are α and 1/α

Now, sum of zeros is given by

$\alpha+\frac{1}{\alpha}=-\frac{b}{a}\\\\\alpha+\frac{1}{\alpha}=-\frac{-10}{3}\\\\\alpha+\frac{1}{\alpha}=\frac{10}{3}...(i)$

And the product of zeros is given by

$\alpha\cdot\frac{1}{\alpha}=\frac{c}{a}\\\\1=\frac{k}{3}\\\\k=3$

Therefore, the value of k is 3.

#Learn More:

Find a quadratic polynomial whose sum and product respectively of these zeros are 2 root 3 and minus 9 also find the zeros of polynomial by factorization

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