The equation, (2x +3/4)^2=-71/6,will have:
(a) two equal real roots
(b) two distinct real roots
(c) no real roots
(d) only one real root
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11th
Maths
Complex Numbers and Quadratic Equations
Quadratic Equations
Which of the following equa...
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Asked on December 30, 2019 by
Niveditha Patil
Which of the following equations has two distinct real roots ?
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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
Answer:
two equal real rootsi hope it may help you