Answer:
see explanation
Step-by-step 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 = - [tex]\frac{5}{6}[/tex]
Solution set = { 1, - [tex]\frac{5}{6}[/tex] }
Answer: The solution set of the given quadratic equation is [tex]\{1,-\dfrac{5}{6}\}.[/tex]
Step-by-step explanation: We are given to find the solution set of the following quadratic equation :
[tex]6a^2-a-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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 :
[tex]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,~-\dfrac{5}{6}.[/tex]
Thus, the solution set of the given quadratic equation is [tex]\{1,-\dfrac{5}{6}\}.[/tex]
