If for a quadratic equation, b2 -4ac=0, then which of the following statements is true? a) roots are real and equal b) roots are not real c) roots are real and unequal d) roots are irrational.
Answers
Answer:
ANSWER
ax
2
+bx+c=0
where a,b,c are rationals
The roots of the above equation are given by the quadratic formula
x=
2a
−b±
b
2
−4ac
Case I
b
2
−4ac<0
Then x=
2a
−b±i
∣b
2
−4ac∣
Thus, both roots are imaginary.
Case II
b
2
−4ac=0
Then the roots are equal and either positive or negative.
Case III
b
2
−4ac>0
b
2
−4ac
>b
Then the roots are real and unequal.
Case IV : b
2
−4ac>0 and perfect square
Then the roots are real, rational and unequal.
If the coefficients are rational, then it is not possible to have one imaginary and one real root.
Case V : b
2
−4ac>0 and not a perfect square
x=
2a
−b±
b
2
−4ac
and b>
b
2
−4ac
⟹ Roots are negative, irrationals and unequal.
Hence, option C is correct.
a ≠ 0 and discriminant is positive
Answer:
But I am not sure about that
Step-by-step explanation:
correct answer is 1