Quadratic EquationEasy
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
View Solution FreeMore Quadratic Equation Questions
The solution set of the inequality $\sqrt{x} - 3 \leq \frac{2}{\sqrt{x} - 2}$ is...Roots of the equation ( a + b − c) x2 − 2ax + ( a− b + c) = 0, ( a,b,c ∈ Q) are -...If the two equations x2 − cx + d = 0 and x2 − ax + b = 0 have one common root and the second has equal roots...If = x − 1, x may have values -...If α, β be the roots of the equation p(x2 + n2) + pnx + qn2x2 = 0 then the value of p (α2 + β2) + p&...