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Question

Question 9
Which of the following equation has two distinct real roots?
(a)
2x232x+94=0
(b) x2+x5=0​​​​​​​
(c) x2+3x+22=0​​​​​​​
(d) 5x23x+1=0​​​​​​​

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Solution

(a)
The given equation is x2 + x – 5 = 0
On comparing with ax2 + bx + c = 0, we get
a = 1, b and c = - 5
The discriminant of x2 + x – 5 = 0 is
D=b24ac=(1)24(1)(5)
= 1 + 20 = 21
b2 - 4ac > 0
So, x2+x5=0 has two distinct real roots
a) Given equation is, 2x232x+94=0
On comparing with ax2 + bx + c = 0\)
a = 2, b =32 and c = 94
Now, D=b24ac=(32)24(2)(94)=1818=0
Thus, the equation has real and equal roots
b) Given equation is x2 + 3x + 2 = 0
On comparing with ax2 + bx + c = 0
a = 1, b =3 and c = 22
now, D=b24ac=(3)24(1)(22)=982<0
Roots of the equation are not real.
c) Given equation is, 5x2 – 3x + 1 = 0
On comparing with ax2 + bx + c = 0
a = 5, b = - 3, c = 1
now, D=b24ac=(3)24(5)(1)=920<0
hence, roots of the equation are not real

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