Can someone tell me how to approach and solve this math problem?

If the pair of lines $6x^2-pxy-3y^2-24x+3y+q=0$ intersect on x- axis then p is equal to :- $a)3/2$ $b)-5/2$ $c)-18$ $d)-7$

Please post the solution in DETAIL...

#Algebra #Geometry #StraightLines

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Sort by:

Top Newest

For 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 !!

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

Deepanshu Gupta - 5 years, 8 months ago

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

Parag Zode - 5 years, 8 months ago

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).

Guiseppi Butel - 5 years, 8 months ago

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 .

Parag Zode - 5 years, 8 months ago

Are there 2 lines? I see only 1 equation.

Guiseppi Butel - 5 years, 8 months ago

The equation above is multiplication of those 2 lines

Krishna Sharma - 5 years, 8 months ago

What are the 2 lines?

Guiseppi Butel - 5 years, 8 months ago

@Guiseppi Butel – That is what we have to find in terms of 'p'

Krishna Sharma - 5 years, 8 months ago

@Krishna Sharma – You also have a q which affects the situation.

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

Guiseppi Butel - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$