Question

f(x) = 4x^2 – 17x + 3What is the value of the discriminant of f?[ ]How many distinct real number zeros does f have?[ ]

Answer 1

f(x) = 4x^2 – 17x + 3

The equation is written in the form:

f(x) = ax^2 + bx + c

Where:

a= 4

b= -17

c= 3

Apply the quadratic formula:

`\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}`

Replace:

`\frac{-(-17)\pm\sqrt[]{(-17)^2-4\cdot4\cdot3}}{2\cdot4}`

The discriminant is the part of the quadratic formula under the square root:

b^2-4*a*c = (-17)^2- (4 * 4 *3 ) = 289- 48 =241

Discriminant = 241

Since the discriminant is greater than zero, the equation has 2 distinct real roots.