Ex 4.3, 1 (iii) - Chapter 4 Class 10 Quadratic Equations

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 4.3, 1
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(iii) 2x2 – 6x + 3 = 0
2x2 – 6x + 3 = 0
Comparing equation with ax2 + bx + c = 0
a = 2, b = –6 , c = 3
We know that
D = b2 – 4ac
= (–6)2 – 4 × 𝟐 × 𝟑
= (–6) × (–6) – 4 × 2 × 3
= 36 – 24
= 12
Since D > 0
There are 2 distinct real roots
Now using quadratic formula to find roots
x = (− 𝑏 ± √𝐷)/2𝑎
Putting values
x = (−(− 𝟔) ± √𝟏𝟐)/(𝟐 × 𝟐)
x = (+ 6 ± √12)/4
x = (6 ± √(4 × 3))/4
x = (6 ± √(4 )× √3)/4
x = (𝟔 ± 𝟐 ×√𝟑)/𝟒
x = (2(3 ± √3))/4
x = (𝟑 ± √𝟑)/𝟐
Therefore, the root of the equation are x = (3 + √3)/2 & x = (3 − √3)/2

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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