Question 14

Find the zeroes of the following polynomial:

5√5 x 2 + 30x + 8√5

 

Here, we solve this question by two methods

  1. Method 1 - Using Splitting the middle term
  2. Method 2 - Using D Formula 

Find the zeroes of polynomial:  5√5 x^2 + 30x + 8√5 - Teachoo

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Transcript

Question 14 (Method 1 – Using Splitting the middle term) Find the zeroes of the following polynomial: 5√5 x2 + 30x + 8√5 5√5 x2 + 30x + 8√5 Factorising by splitting the middle term = 5√5 x2 + 20x + 10x + 8√5 = 5√5 x2 + 20x + (5 × 2)x + 8√5 = 5√5 x2 + 20x + (√5 × √5 × 2)x + 8√5 = 5x(√5 x + 4) + √5 × 2(√5 x + 4) = 5x(√5 x + 4) + 2√5 (√5 x + 4) = (5x + 2√5) (√5x + 4) Splitting the middle term method We need to find two numbers whose Sum = 30 Product = 5√5 × 8 √5 = 5 × 8 × √5 × √5 = 40 × 5 = 200 Zeroes are 5x + 2√5 = 0 5x = –2√5 x = (−𝟐√𝟓)/𝟓 √5x + 4 = 0 √5x = –4 x = (−4)/√5 x = (−4)/√5 × √5/√5 x = (−𝟒√𝟓)/𝟓 √5x + 4 = 0 √5x = –4 x = (−4)/√5 x = (−4)/√5 × √5/√5 x = (−𝟒√𝟓)/𝟓 1 mark Question 14 (Method 2 – Using D formula) Find the zeroes of the following polynomial: 5√5 x2 + 30x + 8√5 5√5 x2 + 30x + 8√5 Comparing with ax2 + bx + c a = 5√5, b = 30, c = 8√5 Now, x = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎 = (−30 ± √(〖(30)〗^2 − 4 × 5√5 × 8√5) )/(2 × 5√5) = (−30 ± √(900 − 4 × 5 × 8 × √5 × √5) )/(10√5) = (−30 ± √(900 − 4 × 5 × 8 × 5))/(10√5) = (−30 ± √(900 −20 × 40))/(10√5) = (−30 ± √(900 − 800))/(10√5) = (−30 ± √100)/(10√5) = (−30 ± 10)/(10√5) 1.5 marks Therefore, x = (−30 + 10)/(10√5) x = (−20)/(10√5) x = (−2)/√5 x = (−2)/√5 × √5/√5 x = (−𝟐√𝟓)/𝟓 x = (−30 − 10)/(10√5) x = (−40)/(10√5) x = (−4)/√5 x = (−4)/√5 × √5/√5 x = (−𝟒√𝟓)/𝟓 . ∴ Zeroes are x = (−𝟐√𝟓)/𝟓, (−𝟒√𝟓)/𝟓 1.5 marks

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.