Question

If root 5 is one of the zeros of the polynomial 5x sq - 3 root 5 x - P then find the value of p.

Answer 1

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Answer 2

$\mathfrak{\huge{Answer:}}$

Given polynomial is : $\sf{p(x) = 5x^{2} -3\sqrt5 x - p =0}$

One of the root of the polynomial is given as : $\sf{\sqrt5}$

Now, as the root is given to be as $\sf{\sqrt5}$, we can keep the value of x as $\sf{\sqrt5}$, in p ( x ). Do the same :

p ( $\sf{\sqrt5}$ ) = $\sf{5(\sqrt5)^{2} - 3(\sqrt5)(\sqrt5) - p = 0}$

Now, try solving this formed equation further :

=》 p ( $\sf{\sqrt5}$ ) => $\sf{(5 \times 5) - (3 \times 5) = p}$

Keep solving this further :

=》 p ( $\sf{\sqrt5}$ ) => $\sf{25 - 15 = p}$

Last one step to go for the answer :

=》 p ( $\sf{\sqrt5}$ ) => p = 10

There's the answer !

Thus, in p ( x ), the value of p = 10

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