Question

What is the discriminate of the following quadratic equation? 4x^2 - 2x + 6 = 0

Answer 1

-92

Step-by-step explanation:

If a quadratic equation has the following form:

$ax^2 + bx + c =0, \;\;\;a \neq 0$

then its discriminant D is defined as

$D = b^2 - 4ac$

In our given quadratic equation, a = 4, b = -2 and c = 6, so its discriminant is

$D = (-2)^2 - 4(4)(6) = -92$

Note: The value of the discriminant D will determine the characteristics of the roots of the quadratic equation according to the following rules:

$D > 0,\;\;$ there will be 2 real roots

$D = 0,\;\;$ there will be 1 real root

$D < 0,\;\;$ there will be 2 imaginary roots

Hence our given quadratic equation will not have any real roots but only imaginary ones.