Question

State the value of the discriminant. Then determine the number of real roots of the equation. –8w2 = –(11w – 7)

Answer 1

No real roots

Explanation:

In order to find the value of the discriminant, we proceed to re-write the quadratic expression with all the terms on one side of the equal sign. First solving the indicated parenthesis preceded by the negative sign, and then by adding
`8w^2` on both sides:

`-8w^(2) = -11w+7\\0=8w^(2) -11w+7`

now we identify the values
`a, b, c` that appear in the expression of the discriminant:
`b^2 -4ac`

These are:

`a=8\\b=-11\\c=7`

Therefore:

`b^2 -4ac=(-11)^2 -4*8*7=121-224=-103`

This is a negative number, which means that the solutions to the quadratic equations are imaginary numbers, and not real numbers.