Which of the following equations has the sum of its roots as 3
a. 2x² - 3x + 6 = 0
b. -x² + 3x - 3 = 0
c. √2x² - 3/√2x + 1 = 0
d. 3x² - 3x + 3 = 0
Solution:
Given, the sum of roots of a quadratic equation is 3.
We have to find the equation.
A quadratic polynomial in terms of the zeroes (α,β) is given by
x2 - (sum of the zeroes) x + (product of the zeroes)
i.e, f(x) = x2 -(α +β) x +αβ ---------------- (1)
From the options,
A) 2x² - 3x + 6 = 0
Dividing by 2,
x² - 3/2x + 3 = 0 ------------------ (2)
Comparing (1) and (2),
α + β = 3/2
Therefore, the sum of the roots of the equation is 3/2.
B) -x² + 3x - 3 = 0
The equation can be written as x² - 3x + 3 = 0 ------------- (3)
By comparing (1) and (3),
α + β = 3
Therefore, the sum of the roots of the equation is 3.
C) √2x² - 3/√2x + 1 = 0
Dividing by √2,
x² - 3/2x + 1/√2 = 0 ------------ (4)
By comparing (1) and (4),
α + β = 3/2
Therefore, the sum of the roots of the equation is 3/2.
D) 3x² - 3x + 3 = 0
Dividing by 3,
x² - x + 1 = 0 -------------------------- (5)
By comparing (1) and (5),
α + β = 1
Therefore, the sum of roots of the equation is 1.
✦ Try This: Which of the following equations has the sum of its roots as 3?
a. 2x² - 3x + 6 = 0
b. x² + 3x - 9 = 0
c. √2x² - 3/√2x + 1 = 0
d. 3x² - 3x + 3 = 0
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.1 Problem 5
Which of the following equations has the sum of its roots as 3, a. 2x² - 3x + 6 = 0, b. -x² + 3x - 3 = 0, c. √2x² - 3/√2x + 1 = 0, d. 3x² - 3x + 3 = 0
Summary:
The equation -x² + 3x - 3 = 0 has the sum of the roots as 3.
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