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If p and q are the roots of the quadratic equation ax2 + bx + c = 0 where a ≠ 0, what are the roots of the equation ayx2 + byx + cy = 0 where 0 < y ≤ 1?
- a)p and q
- b)py and qy
- c)p/yand q/y
- d)y and -y
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If p and q are the roots of the quadratic equation ax2 + bx + c = 0 wh...
Given
- ax2+bx+c=0
- has two roots p and q a ≠ 0, 0 < y ≤ 1
To Find
- Roots of ayx2+byx+cy=0
Approach
- To find the roots of the equation ayx2+byx+cy=0 , we will do the following steps:
- Take y common and the get the equation in terms of ax2+bx+c=0
- As we know the roots of ax2+bx+c=0, we will use this knowledge to find the roots of the equation ayx2+byx+cy=0
- Working OutSolving the equation ayx2+byx+cy=0
- ayx2+byx+cy=0
- y(ax2+bx+c)=0
So we have either y = 0 or ax2+bx+c=0
Since we are given that y > 0, y ≠ 0.
Hence ax2+bx+c=0
.As the roots of the equation ax2+bx+c=0 are p and q, the roots of the equation ayx2+byx+cy=0 will also be p and q.
Answer: A
Most Upvoted Answer
If p and q are the roots of the quadratic equation ax2 + bx + c = 0 wh...
Solution:
Given, the roots of the equation ax2 bx c = 0 are p and q.
We know that the sum of the roots of the quadratic equation ax2 bx c = 0 is given by -b/a and product of the roots is given by c/a.
Therefore, we have:
p + q = -b/a
pq = c/a
Multiplying the given equation ayx2 byx cy = 0 by y, we get:
ayx2 byx cy = 0
ay2x2 bxy cy = 0
The roots of the above equation will be given by:
y(p + q)/2 and y(pq)
Substituting the values of p + q and pq from the given quadratic equation, we get:
y(p + q)/2 = y(-b/2a) = -(by)/2a
ypq = (cy)/a
Therefore, the roots of the equation ayx2 byx cy = 0 are:
-(by)/2a and cy/a
Hence, option A is the correct answer.
Given, the roots of the equation ax2 bx c = 0 are p and q.
We know that the sum of the roots of the quadratic equation ax2 bx c = 0 is given by -b/a and product of the roots is given by c/a.
Therefore, we have:
p + q = -b/a
pq = c/a
Multiplying the given equation ayx2 byx cy = 0 by y, we get:
ayx2 byx cy = 0
ay2x2 bxy cy = 0
The roots of the above equation will be given by:
y(p + q)/2 and y(pq)
Substituting the values of p + q and pq from the given quadratic equation, we get:
y(p + q)/2 = y(-b/2a) = -(by)/2a
ypq = (cy)/a
Therefore, the roots of the equation ayx2 byx cy = 0 are:
-(by)/2a and cy/a
Hence, option A is the correct answer.
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If p and q are the roots of the quadratic equation ax2 + bx + c = 0 where a ≠ 0, what are the roots of the equation ayx2 + byx + cy = 0 where 0 < y ≤ 1?a)p and qb)py and qyc)p/yand q/yd)y and -ye)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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