If x²+5x+6= (x+a) (x+a), then find the value of a+b.
Answers
Answer:
x²+5x+6
x²+3x+2x+6
x(x+3)+2(x+3)
(x+3)(x+2)
comparing with (x+a)(x+b) we get
a=3 and b=2
Answer:
Okay, as you can see it's 2 degree polynomial and the highest power of x is 2. Thus, there are 2 values of x for which we'll get to satisfy the given equation.
Now,
x^2–5x+6=0 is comparable with ax^2+bx+c=0, where a=1 ,b =-5 and c=6 .
In this case, you'll have to split b in such a way that the factors of the product a and c, i.e. (ac) will correspond to b and further factorise them. You can add the factors or even substract them to get b.
A.T.Q.
x^2–5x+6=0
We have ac=6. Thus, we'll have to split 6 in such a way that we will get 5.
Webcan do it in 2 ways,(6–1) and (3+2).
So,
x^2-(6–1)x+6=0
=> x^2–6x+x+6=0
=> x(x-6)+1(x+6)=0
But, as we can see, we cannot proceed further.
So let's try the other option we have
x^2–5x+6=0
=>x^2-(3+2)x+6=0
=>x^2–3x-2x+6=0
=>x(x-3)-2(x-3)=0
=>(x-3)(x-2)=0
This means that either of them will be zero, so again we have two possibilities, where
Either,
x-3=0
=>x=3
Or,
x-2=0
=>x=2.
Thus, the possible values of x are 2 and 3.
Step-by-step explanation:
hope it helps you