Question

Let for a≠a1≠0 f(x) = ax^2 + bx + c, g(x)= a1x^2 + b1X + C1and p(x) = f(x) – g(x). If p(x) = 0 only for x=-1 and p(-2) = 2, then the value of p(2) is


(1)3
(2)9
(3) 6
(4) 18


serious answers only​

Answer 1

Answer:

Correct option is

B

18

Given, f(x)=ax

2

+bx+c,g(x)=ax

2

+bx+c,

and p(x)=f(x)−g(x)

p(x)=0 for only x=−1,p(−2)=2 and a



=a

1



=0

∴p(x)=(a−a

1

)x

2

+(b−b

1

)x+(c−c

1

)

The standard quadratic equation is ax

2

+bx+c=0

For roots to be equal ⇒b

2

−4ac=0

Then Sum of roots = −

a

b

Here, Only root is −1⇒D=0⇒(b−b

1

)

2

=4(a−a

1

)(c−c

1

)→(1)

Sum of roots ⇒(−1)+(−1)=

(a−a

1

)

−(b−b

1

)

⇒(b−b

1

)=2(a−a

1

)→(2)

From (1) and (2), c−c

1

=(a−a

1

)→(3)

⇒p(x)=(a−a

1

)x

2

+2(a−a

1

)x+(a−a

1

)

Now, p(−2)=2

⇒2=(a−a

1

)(−2)

2

−2(a−a

1

)(−2)+(a−a

1

)

⇒(a−a

1

)=2

Now p(2)=2(2)

2

+2(2)(2)+2=18