Question

Determine which functions have two real number zeros by calculating the discriminant, b2 – 4ac. check all that apply. f(x) = x2 6x 8 g(x) = x2 4x 8 h(x) = x2 – 12x 32 k(x) = x2 4x – 1 p(x) = 5x2 5x 4 t(x) = x2 – 2x – 15

Answer 1

Function f(x), h(x), k(x) and t(x) will have real roots while function g(x) and p(x) will have imaginary roots.

Given quadratic functions are:

$1) f(x)= x^{2} +6x+8\\2)g(x) = x^{2} +4x+8\\3)h(x) = x^{2} -12x+32\\4)k(x)=x^{2} +4x-1\\5)p(x)=5x^{2} +5x+4\\6)t(x) = x^{2} -2x-15$

What is the general form of a quadratic equation?

The general form of a quadratic equation is:

$ax^{2} +bx+c=0$

On comparing $x^{2} +6x+8 =0$ with the general form,

a=1, b=6, c=8

If discriminant D=b²-4ac is greater than zero, the quadratic equation will have two distinct real roots, if D is less than zero, roots will be imaginary.

So, discriminant D for f(x)=0 will be:

$b^{2} -4ac$ = $6^{2} -4*1*8 = 4$ i.e. greater than zero.

So, the quadratic function $f(x) = x^{2} +6x+8$ will have two real distinct

roots.

Similarly, h(x), k(x), and t(x) will have real roots since their discriminants are greater than zero.

Thus, Function f(x), h(x), k(x) and t(x) will have real roots while function g(x) and p(x) will have imaginary roots.

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