Question

The solution set for 6a2 - a -5 = 0 is

Answer 1

see explanation

Explanation:

Given

6a² - a - 5 = 0

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a- term.

product = 6 × - 5 = - 30 and sum = - 1

The factors are - 6 and + 5

Use these factors to split the a- term

6a² - 6a + 5a - 5 = 0 ( factor the first/second and third/fourth terms )

6a(a - 1) + 5(a - 1) = 0 ← factor out (a - 1) from each term

(a - 1)(6a + 5) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

6a + 5 = 0 ⇒ 6a = - 5 ⇒ a = -
`(5)/(6)`

Solution set = { 1, -
`(5)/(6)` }

Answer 2

Answer: The solution set of the given quadratic equation is
`\{1,-(5)/(6)\}.`

Step-by-step explanation: We are given to find the solution set of the following quadratic equation :

`6a^2-a-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be solving the given quadratic equation by the method of FACTORIZATION.

To factorize the expression on the L.H.S. of equation (i), we need two integers with sum -1 and product -30. Those two integers are -6 and 5.

The solution of equation (i) is as follows :

`6a^2-a-5=0\\\\\Rightarrow 6a^2-6a+5a-5=0\\\\\Rightarrow 6a(a-1)+5(a-1)=0\\\\\Rightarrow (a-1)(6a+5)=0\\\\\Rightarrow a-1=0,~~~~~~6a+5=0\\\\\Rightarrow a=1,~-(5)/(6).`

Thus, the solution set of the given quadratic equation is
`\{1,-(5)/(6)\}.`