Algebra , Polynomials

Algebra Level 2

If one zero of the polynomial $({ a }^{ 2 }+9){ x }^{ 2 }\quad +\quad 13x\quad +\quad 6a$ is reciprocal of the other , then find the value of a and enter.

The answer is 3.

3 solutions

Kevin Patel
Jul 16, 2014

Since they are reciprocal of each other, (A²+9) = 6A which is satisfied when A=3.

Sanchayapol Lewgasamsarn
Jun 4, 2014

Let $m$ and $n$ be the two roots of the polynomial.

We will get that $mn = 1$ because $n$ is a reciprocal of $m$ and vice versa.

By Vieta's Formula,

$mn = 1 = \frac{6a}{a^{2} + 9}$

Solve the quadratic equation and $a = 3$ is our final answer.

Jayakumar Krishnan
Jun 1, 2014

Using the simple formula of quadratic equations, we get that a*1/a= 1= 6a/a^2+9. This gives us the relation that a= 3 when you solve it :)

but whn a=3 the equation : 18x^2+13x+18=0 has no real roots !!

Kimo El-ghazawy - 7 years ago

The problem did not state that the roots are real. :P

Sanchayapol Lewgasamsarn - 7 years ago

Algebra , Polynomials

The answer is 3.

3 solutions

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