HiSET - Identification | Practice Hub

The equation

$x^{2} + 34 = 17x$

has two distinct solutions. What is their sum?

Explanation

It is not necessary to actually find the solutions to a quadratic equation to determine the sum of its solutions.

First, get the equation in standard form $ax^{2}+ bx + c = 0$ by subtracting from both sides:

$x^{2} + 34 = 17x$

$x^{2} + 34 -17x = 17x - 17x$

$x^{2} -17x + 34 = 0$

If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient . In this problem, , making the correct choice.

The graph of the polynomial function

$f(x)= x^{3}+x^{2}-5x+2$

has one and only one zero on the interval . On which subinterval is it located?

Explanation

The Intermediate Value Theorem (IVT) states that if the graph of a function is continuous on an interval , and and differ in sign, then has a zero on . Consequently, the way to answer this question is to determine the signs of on the endpoints of the subintervals - $\left { 0, 0.2, 0.4, 0.6, 0.8, 1 \right }$ . We can do this by substituting each value for as follows: