Question

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

Answer 1

Answer:

No real roots

Step-by-step 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.