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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 equation6x2−24x+q=0 should be perfect square ? If it is then the value of q is equal to 24. This is a JEE Question .
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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.
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Top NewestFor to intersect this pair of straight line on x-axis , Let They intersect at point P (α0 )
So putting y=0 in given equation
6α2−24α+q=0.
Now since Intersection point is unique so value of α is also unique. So Discriminant of this quadratic equation is zero !!
q=24α=2.
Therefore Given equation representing pair of straight lines if it's Discriminant is zero !!
∣∣∣∣∣∣6−p/2−12−p/2−33−123/224∣∣∣∣∣∣=0P=3/2.
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Ok! I didn't knew to use determinant after finding q and a(alpha).. Anyways ,Nice solution.
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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).
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Sir but can we assume that for finding value of q the equation6x2−24x+q=0 should be perfect square ? If it is then the value of q is equal to 24. This is a JEE Question .
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Are there 2 lines? I see only 1 equation.
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The equation above is multiplication of those 2 lines
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What are the 2 lines?
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If this line intersects the x axis then the value for y = 0.
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