The line(s) intersect the x-axis when y=0.
The equation then becomes 6x^2 - 24x + q = 0.
There are tons of values for x that will solve this equation depending on the value of q.

If y = 0 then values for p are limitless (infinite).

Sir but can we assume that for finding value of q the equation$6x^2-24x+q=0$ should be perfect square ? If it is then the value of q is equal to 24. This is a JEE Question .

$</code> ... <code>$</code>...<code>."> Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestFor to intersect this pair of straight line on x-axis , Let They intersect at point P ($\alpha \, 0$ )

So putting y=0 in given equation

$6\alpha ^{ 2 }\quad -\quad 24\alpha \quad +\quad q\quad =\quad 0$.

Now since Intersection point is unique so value of $\alpha$ is also unique. So Discriminant of this quadratic equation is zero !!

$q\quad =\quad 24\\ \\ \alpha \quad =\quad 2$.

Therefore Given equation representing pair of straight lines if it's Discriminant is zero !!

$\left| \begin{matrix} 6 & -p/2 & -12 \\ -p/2 & -3 & 3/2 \\ -12 & 3 & 24 \end{matrix} \right| \quad =\quad 0\\ \\ P\quad =\quad 3/2$.

Log in to reply

Ok! I didn't knew to use determinant after finding q and a(alpha).. Anyways ,Nice solution.

Log in to reply

The line(s) intersect the x-axis when y=0. The equation then becomes 6x^2 - 24x + q = 0. There are tons of values for x that will solve this equation depending on the value of q.

If y = 0 then values for p are limitless (infinite).

Log in to reply

Sir but can we assume that for finding value of q the equation$6x^2-24x+q=0$ should be perfect square ? If it is then the value of q is equal to 24. This is a JEE Question .

Log in to reply

Are there 2 lines? I see only 1 equation.

Log in to reply

The equation above is multiplication of those 2 lines

Log in to reply

What are the 2 lines?

Log in to reply

Log in to reply

If this line intersects the x axis then the value for y = 0.

Log in to reply