Without actually solving, determine the number of zeros. Explain your answer (Use the Discriminant)

Question

a) f(x) = 2x^2 -6x -7

b) 2x^2 = -8x - 3

Answer 1

Follow this rule:

When the discriminant (b² - 4ac) is greater than 0, there are two distinct real roots.

When the discriminant is equal to 0, there is exactly one real root.

When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots.

a) 2x² -6x -7 a = 2, b = -6, c= -7 (use b² - 4ac and plug a, b, c)

b)2x² = -8x -3; we need to convert this to quadratic form add 8x+3 both sides

2x² +8x +3 = 0; determine a, b, c and plug them in to the formula b² - 4ac

Hope that helps