Question 2 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Let p be a prime number. The quadratic equation having its roots as factors of p is

(a) x
^{
2
}
– px + p = 0

(b) x
^{
2
}
– (p + 1)x + p = 0

(c) x
^{
2
}
+ (p + 1)x + p = 0

(d) x
^{
2
}
– px + p + 1=0

Transcript

Question 2 Let p be a prime number. The quadratic equation having its roots as factors of p is (a) x2 – px + p = 0 (b) x2 – (p + 1)x + p = 0 (c) x2 + (p + 1)x + p = 0 (d) x2 – px + p + 1=0We need to find quadratic equation having its roots as factors of p is
Since p is a prime number
Factors of p = 1, p
Thus, we need to find quadratic equation with roots 1 and p
Required quadratic equation is
x2 − (Sum of roots)x + Product of roots = 0
Putting values
𝑥^2−(1+𝑝)𝑥+(1 × 𝑝)=0
𝒙^𝟐−(𝟏+𝒑)𝒙+𝒑=𝟎
So, the correct answer is (b)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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