CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard

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Question 27 - 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

If the zeroes of the polynomial x 2 + px +q are double in value to the zeroes of the polynomial 2x 2 – 5x – 3, then find the values of p and q.

 

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Transcript

Question 27 If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.Given that zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, Finding zeroes of 2x2 – 5x – 3 2x2 − 5x − 3 = 0 Solving by Spitting the middle term 2x2 − 6x + x − 3 = 0 2x(x − 3) + 1(x − 3) = 0 (2x + 1) (x − 3) = 0 Splitting the middle term method We need to find two numbers whose Sum = −5 Product = 2 × −3 = −6 Therefore, x = (−𝟏)/𝟐, x = 3 Since zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3 Therefore, Zeroes of polynomial x2 + px + q = 2 × (−𝟏)/𝟐, 2 × 3 = −1, 6 Let’s find quadratic equation with zeroes −1 and 6 Required quadratic equation is x2 − (Sum of roots)x + Product of roots = 0 Putting values x2 − (−1 + 6)x + (−1 × 6) = 0 x2 − 5x − 6 = 0 Comparing with x2 + px + q ∴ p = −5, q = −6

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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.