Very-Short-Answer Questions

Question:

Very-Short-Answer Questions

If the roots of the quadratic equation $p x(x-2)+6=0$ are equal, find the value of $p$.

 

Solution:

It is given that the roots of the quadratic equation $p x^{2}-2 p x+6=0$ are equal.

$\therefore D=0$

$\Rightarrow(-2 p)^{2}-4 \times p \times 6=0$

$\Rightarrow 4 p^{2}-24 p=0$

$\Rightarrow 4 p(p-6)=0$

$\Rightarrow p=0$ or $p-6=0$

$\Rightarrow p=0$ or $p=6$

For p = 0, we get 6 = 0, which is not true.

∴ p ≠ 0

Hence, the value of p is 6.

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