Compute the value of the discriminant and give the number of real solutions of the quadratic equation. 2x^2-8x+1=0

Answer 1

For the quadratic equation given by:

ax^2 + bx + c = 0

the answer (x) is given by:

The discriminant is given by the portion under the radical:

b^2 - 4ac

This discriminant tells us about the nature of the roots (values of x). If it is negative then you will be taking the square root of a negative number which is not a real number, In that case, the roots are imaginary (and there are 2 of them).

If the discriminant is equal to zero, since the square root of zero is zero, there will be just 1 answer, x = -b/(2a).

If the discriminant is a positive number, there will be two real root answers.

In this case the discriminant is:

[ (-8)^2 -4(2)(1)] = 64 - 8 = 56

so there are two real root solutions.