The problem says that 6x squared+7x-20fits the formula ax squared+bx+c. It then asks'what is a?' I want to know if a would be 6?
Let f(x) = 6x^2 + 7x - 10
The standard for the equation is
f(x) = ax^2 + bx + c
a = 6
b = 7
To test if a is equal to 6, we have to take the original equation which is 6x^2+7x-20=ax^2+bx+c and substitute a with 6.
As the terms that x^2 and x are multiplied with and the constant term on both the sides must be the same:
6x^2+7x-20=6x^2+bx+c verifies that a=6.
We also get that b=7 and c=-20.
For this equation a=6, b=7 and c=-20.
6x^2+7x-20 fits the formula ax^2+bx+c.
To find a.
6x^2+7x-20 fits the formul ax^2+bx+c, when
6x^2+7x-20 = ax^2+bx+c .........(1)identitically.
That means for all vlues of x (1) should hold.
That means, ax^2+bx+c-(6x^2+7x-20) = 0 for all values of x.
That means (a-6)x^2+(b-7)x+(c+20) = 0 for all values of x.
That is possible only when (a-6) =0 and b-7 = 0 and c+20 = 0
Therefore it requires a = 6 and b= 7 and c=-20 holds true together.