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The quadratic equations $x + 4 2 – 8 x = 0$ have two distinct real roots.

State true (T) or false (F).

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True

False

answer is B.

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Detailed Solution

The given equation is

x + 4 2 – 8 x = 0

.
If a quadratic equation

a x 2 + b y + c = 0

has the value of

D = b 2 − 4 a c > 0

, then it has two distinct roots.
If a quadratic equation

a x 2 + b y + c = 0

has the value of

D = b^{2} - 4 ac < 0

, then it has imaginary roots.
Solving the equation,

⇒ x 2 + 16 + 8 x – 8 x = 0 ⇒ x 2 + 16 = 0 ⇒ x 2 + 0. x + 16 = 0

Then, on comparing we get,
a = 1, b = 0 and c = 16
So,

D = b 2 − 4 a c

= (0) – 4 (1) (16)
= – 64 < 0.
Thus, the equation has imaginary roots.
Therefore, the given statement, “The quadratic equations

x + 4 2 – 8 x = 0

have two distinct real roots.” is false.

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