Question

p(x)=x2-3x+2a, g(x)= x2-5x+b and p(2)=0, g(2)=0 then find a+b.​

Answer 1

Introduction and a small tip

For those of you who think that this question is tough or confusing, this question is absolutely easy. if i am correct this question has been asked from the chapter polynomials of CBSE maths class 9 or 10. don't be scared first of all we we should always do maths with a relaxed mind. Calm down Take a deep breathe and then attempt the questions with confidence.

I am Sorry for wasting your time

Let's Start...

Answer:

a=1

b=6

Therefore, a+b=6+1=7

Rearrangement and organising of the question

First let me tell you that this question is actually two questions connected together by a small piece of wire. How is it??. Let's see

It's given in the question that

' p(x)=x2-3x+2a, g(x)= x2-5x+b and p(2)=0, g(2)=0 then find a+b.'

Here always remember that p(x) and g(x) are two separate equations. In fact there is no relation between p(x) and g(x) in this question. the only small piece of wire which connects them is the variable a in p(x) and the variable b in g(x) and that we have to find the sum of a and b (a+b). So, the first step which we will do is dividing this question into two parts I.e

1) p(x)=x2-3x+2a and p(2)=0

2) g(x)= x2-5x+b and g(2)=0

Now this question looks a lot simpler and organized

Let's start...

Solution:

Let's look at the first part

1) p(x)=x2-3x+2a and p(2)=0

Here we have been given a value of p(x) and we have also been given that p(2)=0. So using pure logic and common sense what simple thing can we find in this question?? what connects the two equations or sentences or anything that you can assume?????

Think About it....

Think

Think

Think

Think

Think

Think

If you got it then very well done

If you didn't scroll down below

Its very simple!!

Even LKG students can find it

What is given to us??

p(x)=x2-3x+2a and p(2)=0

This simply means that if in p(x) if we substitute 2 in place of x in all places where x is in the equation p(x) we will get zero as the result

So what's next ??

Simple!!

Let's write 2 in all the places where x is in the equation p(x).

That will be

p(x)= (2)^2 -3(2)+2a. (We don't what the value of a is yet)

since we have wrote two in places of x instead of p(x) we will write it as p(2)

So let's continue

p(2)= 4-6+2a

p(2)= (-2) +2a. ( Don't forget that 4-6 is (-2) not 2)

since p(2) is zero we will write zero in place of that

0= (-2) + 2a

Now this is a very simple linear equation in two variables

Let's solve it...

Take (-2) to the other side

Assuming that all if you know how to solve linear equations I will do it

2=2a

a=2/2 that is a=1

let's check if p(2) and a=1 gives is zero

p(2)= (2)^2 -3(2)+2(1)

p(2)= 4-6+2

p(2)= 6-6

p(2)=0

Hence we have verified that a=1

So we have completed the first part of three parts of this question (if you are wondering what the third part is , the third part us finding the sum of a and b i. e a+b)

Let's move onto the second part

2) g(x)= x2-5x+b and g(2)=0

Again if we use simple logic and common sense we can see that if we write 2 instead of x in all the places of x in the equation g(x) we will get 0 as the result

So what's next??

Let's do it.....

g(2)= 2^2 -5(2)+b

since g(2) is zero we will write zero in place of that

0= 2^2 -5(2)+b

0=4-10+b

0=(-6) + b

Just take (-6) to the other side and you will find that

b=6

Let's check if our solution is correct

Let's check g(2) and b=6 gives us zero

g(2)= 2^2-5(2)+6

g(2)=4-10+6

With simple addition and subtraction we can see that

g(2)=10-10

g(2)=0

Hence we have verified our answer that b=6

So the second part of our answer is also over

Now let's look at the last and the concluding part which is the final answer

3) a+b=??

Now that we know that a=1 and b=6

let's find out the sum of a and b

I think I don't need to elaborate this so I will move forward

a+b=6+1=7

a+b=7

Finally.. the answer

So I Hope that those of you who chose the first option which I gave in the beginning, I hope that you have understood this question. I am reminding you that you don't need to explain like this in the exam . I have attached some photos which include the solution, verification and final answer.

Hope it helps

Thank you

Have a nice day

Answer 2

a + b = 1 + 6 = 7 is your answer.