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Question 5
Which of the following equations has the sum of its roots as 3?
(a) 
2x23x+6=0
(b) x2+3x3=0
(c) 2x232x+1=0​​​​​​​ 
(d) 
3x23x+3=0​​​​​​​


Solution

a) Given that, 2x23x+6=0
On comparing with ax2 + bx + c = 0, we get
a = 2, b = 3  and c = 6
Sum of the roots =ba(3)2=32
So, sum of the roots of the quadratic equation 2x2 – 3x + 6 = 0 is not 3, so it not the answer
b) Given that, x2 + 3.x – 3 = 0
On compare with ax2 + bx + c = 0, we get
a = -1, b = 3 and c  = - 3
sum of the roots  =ba=(3)1=3
So, sum of the roots of the quadratic equation x2 + 3.x – 3\) is 3, so it is the answer
c) Given that  2x232x+1=0
2x23x+2=0
On comparing with ax2 + bx + c = 0, we get
a = 2, b = - 3  and c = 2
sum of the roots  =ba=(3)2=32
so, sum o f the roots of the quadratic equation 2x232x+1=0 is not 3, so it is not the answer
d) Given that, 3x2 – 3x + 3 = 0
x2x+1=0
On comparing with ax2 + bx + c = 0  get
a = 1 b = - 1 and c = 1
sum of the roots =ba=(1)1=1
So, sum of  the roots of the quadratic equation 3x2 + 3 = 0 is not 3, so it is not the answer

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