What is the discriminant of $2 x^{2} = 4 x - 7$ $2x^2 = 4x - 7$ and what does that mean?

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What is the discriminant of $2 x^{2} = 4 x - 7$ $2x^2 = 4x - 7$ and what does that mean?

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Answer 1 · 2018-05-30T06:24:09

In the equation $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ , the discriminant is $b^{2} - 4 a c$ $b^2-4ac$

Explanation:

By completing the square it is possible to see that the solutions of the equation:

$a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

are of the form:

$x_{1}$ $x_1$ = $\frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b + sqrt(b^2-4ac))/(2a)$ and

$x_{2}$ $x_2$ = $\frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b - sqrt(b^2-4ac))/(2a)$

So, to have solutions in the real numbers (as opposed to complex numbers), the square root $\sqrt{b^{2} - 4 a c}$ $sqrt(b^2-4ac$ must exist as a real number, and so we need $b^{2} - 4 a c \geq 0$ $b^2-4ac>=0$ .

In summary, to have real solutions, the discriminant $b^{2} - 4 a c$ $b^2-4ac$ of the equation must satisfy $b^{2} - 4 a c \geq 0$ $b^2-4ac>=0$

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What is the discriminant of $2 x^{2} = 4 x - 7$ $2x^2 = 4x - 7$ and what does that mean?

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Explanation:

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