if roots of the quadratic equation bx^2 -2ax+a=0 are real and distinct, where a,b belong to real numbers and b !=0,then
(a) at least one root lies in the interval (0,1)
(b) no root lies in the interval (0,1)
(c) at least one root lies in the interval (-1,0)
(d) none of the above
Answers
Answered by
1
Answer:
Roots of the quadratic equation ax
2
+bx+c=0 are imaginary.
⇒b
2
−4ac<0 -----(1)
Now, for the expression a
2
x
2
+abx+ac,
Δ=a
2
b
2
−4a
3
c=a
2
(b
2
−4ac)<0 from (1)
Since, discriminant value is less than zero, coefficient of x
2
and expression always have same sign.
∴a
2
x
2
+abx+ac>0
Hence, option A.
Answered by
0
Answer:
Roots of the quadratic equation ax
2
+bx+c=0 are imaginary.
⇒b
2
−4ac<0 -----(1)
Now, for the expression a
2
x
2
+abx+ac,
Δ=a
2
b
2
−4a
3
c=a
2
(b
2
−4ac)<0 from (1)
Since, discriminant value is less than zero, coefficient of x
2
and expression always have same sign.
∴a
2
x
2
+abx+ac>0
Hence, option A.
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