Question

Which equation could be used to find the zeros of the function f(x) = 6x2-11x-10 = 0 ? (x+2)(x-5) = 0 (3x+2)(2x-5) = 0 (x-10)(x-1) = 0 (2x+3)(3x-4) = 0

Answer 1

Answer:

(3x+2)(2x-5) = 0

Step-by-step explanation:

In the multiple choice options, all of the answers are in factored form. Factored from for quadratic equations are used to find the zeroes, when you equate each factor to 0.

Remember quadratic equations are in the form ax² + bx + c = 0.

Factor 6x² - 11x - 10 = 0:

I will use the cross factors or "X" method.

Write out the factors for "a" and "c" vertically (see diagram 1).

Test a pair of factors from "a" and a pair of factors from "c". Cross multiply them and add their products. If the sum of their products is "b", you found the factors.

The value of "b" is -11.

Example 1: (diagram 2)

I will try if the highlighted pairs of factors work. Multiply the pairs diagonally, which gives me "1" and "-60". The sum of "1" and "-60" is -59.

-59 is not -11; this is not the pair we want.

Example 2: (diagram 3)

Try another pair. Multiply 2*5=10 and 3*-2= -6. Add them together; -6 + 10 = 4.

4 is not -11; this is also wrong.

Example 3: (diagram 4)

Multiply 2*2=4 and 3*-5= -15.

Add the answers: 4 + (-15) = -11.

-11 is "b". Keep these factor pairs.

Find the factors: (diagram 5)

The factors are found by reading across the top and the bottom. Include "x" with the first factor.

(2x-5)(3x+2) = 0  or (3x+2)(2x-5) = 0