Quadratic EquationHard
Question
If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is
Options
A.greater than 4ab
B.less than 4ab
C.greater than - 4ab
D.less than - 4ab
Solution
bx2 + cx + a = 0
Roots are imaginary ⇒ c2 - 4ab < 0 ⇒ c2 < 4ab ⇒ - c2 > - 4ab
3b2x2 + 6bcx + 2c2
since 3b2 > 0
Given expression has minimum value
Minimum value
= - c2 > - 4ab.
Roots are imaginary ⇒ c2 - 4ab < 0 ⇒ c2 < 4ab ⇒ - c2 > - 4ab
3b2x2 + 6bcx + 2c2
since 3b2 > 0
Given expression has minimum value
Minimum value
= - c2 > - 4ab. Create a free account to view solution
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