Question

for what value of p the equation px​2- 18x +1=0 is a perfect square.

Answer 1

given quadratic equation is perfect square

iff its roots are equal

${b}^{2} - 4ac = 0$
$324 - 4p = 0$
$p = 81$

Answer 2

Answer:

The value of p in the equation $p x^2-18 x+1=0$ is 81.

Explanation:

Given equation:

$p x^2-18 x+1=0$

and we know that the given equation is a perfect square.

So, the discriminant of the given equation is 0.

That means:

$b^2-4 a c=0$

where,

$\begin{aligned}& a=p; b=-18; c=1; \\& \Rightarrow b^2-4 a c=(-18)^2-4 \times p \times 1=0 \\& \Rightarrow 324=4 \times p \\& \Rightarrow p=\frac{324}{4}=81\end{aligned}$

Hence,

The value of p in the equation is 81.

To learn more about equations, visit:

https://brainly.in/question/48534636

To learn more about discriminant, visit:

https://brainly.in/question/51975632

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