Let $a, b$ and c be the real numbers such that $4 a + 2 b + c = 0$ and $ab > 0$ Then the equation $a x^{2} + bx + c = 0$ has,

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complex roots

exactly one root

real roots

none of these

answer is C.

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Detailed Solution

The standard quadratic equation can be given as,

a x^{2} + bx + c = 0

Assume the value

x = 2

in the above equation, so we get,

a {(2)}^{2} + b (2) + c = 0

4 a + 2 b + c = 0

This implies that the given quadratic equation's real root can equal two.
Now, polynomial equation's degree = number of its roots
So, quadratic equation

a x^{2} + bx + c = 0

has two roots.
Here, we have quadratic equation which has one real root which is 2.
So, the other root should also be real.
As a result, the provided quadratic equation has real and distinct roots.
So, option 3 is correct.

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