Question

Ini
1.Which of the following equations has two distinct real roots?
(a) 2x2-3v2x+9/4 =0 (b) x + x-5 =0 (c) ** +3x +212 =0 (d) 5 x2 - 3x +1 =0​

Answer 1

Answer:

An equation is said to have two distinct and real roots if the discriminant b

2

−4ac>0

Case (i): For equation: 2x

2

−3

2

x+

4

9

=0.

Here a=2,b=−3

2

,c=

4

9

The discrimant is (−3

2

)

2

−4(2)(

4

9

)=18−18=0

Hence this equation has equal real roots

Case (ii): For equation: x

2

+x−5=0.

Here a=1,b=1,c=−5

The discrimant is 1

2

−4(1)(−5)=1+20=21>0

Hence this equation has two distinct real roots

Case (iii): For equation: x

2

+3x+2

2

=0.

Here a=1,b=3,c=2

2

The discrimant is 3

2

−4(1)(2

2

)=9−8

2

<0

Hence this equation has no real roots

Case (iv): For equation: 5x

2

−3x+1=0.

Here a=5,b=−3,c=1

The discrimant is (−3)

2

−4(5)(1)=9−20<0

Hence this equation has no real roots