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Question : If the equation k(21x+ 24) + rx + (14x– 9) = 0, k(7x+ 8) + px + (2x– 3) = 0 have both roots common, then the value of $\frac{p}{r}$ is:

Option 1: $\frac{1}{3}$

Option 2: $\frac{2}{5}$

Option 3: $\frac{4}{3}$

Option 4: $\frac{7}{5}$


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: $\frac{1}{3}$


Solution : Since the roots of the equation are common, the coefficients are in proportion.
The equation 1 can be written as, (21k +14)x 2 + rx + 24k – 9 = 0
The equation 2 can be written as, (7k + 2)x 2 + px + 8k – 3 = 0
Therefore,
$\frac{21k+14}{7k+2} = \frac{r}{p} = \frac{24k-9}{8k-3}$
$⇒\frac{r}{p} = \frac{24k−9}{8k−3}$
$⇒\frac{r}{p} = \frac{3 \times (8k−3)}{(8k−3)}$
$⇒\frac{r}{p} = \frac{3}{1}$
$\therefore\frac{p}{r}=\frac{1}{3}$
Hence, the correct answer is $\frac{1}{3}$.

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