Let $f(x)=x^2+ax+b$ and $g(x)=f(x+1)-f(x-1)$ . If $f(x)≥0$ for all real $x$ , and $g(20)=72$ , then the smallest possible value of $b$ is

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Let  $f(x)=x^2+ax+b$  and  $g(x)=f(x+1)-f(x-1)$ . If  $f(x)≥0$  for all real  $x$ , and  $g(20)=72$ , then the smallest possible value of  $b$  is

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The correct answer is (D):  $4$ $f(x)=x^2+ax+b$ $g(x)=f(x+1)-f(x-1)$ = ${(x+1)^2+a(x+1)+b}-{(x-1)^2+a(x-1)+b}$ $g(x)=4x+2a$ $g(20)=72$ $80+2a=72 ⇒ a=-4$ $∴ f(x)=x^2-4x+b$ $f(x)=(x-2)^2+b-4$ When  $b≥4 f(x)≥0$  for all  $x$ $∴$  The minimum value of b is  $4$

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Let $f(x)=x^2+ax+b$ and $g(x)=f(x+1)-f(x-1)$ . If $f(x)≥0$ for all real $x$ , and $g(20)=72$ , then the smallest possible value of $b$ is

The Correct Option is D

Solution and Explanation

Top Questions on Functions

Questions Asked in CAT exam

Let f(x)=x2+ax+bf(x)=x^2+ax+bf(x)=x2+ax+b and g(x)=f(x+1)−f(x−1)g(x)=f(x+1)-f(x-1)g(x)=f(x+1)−f(x−1). If f(x)≥0f(x)≥0f(x)≥0 for all real xxx, and g(20)=72g(20)=72g(20)=72, then the smallest possible value of bbb is

The Correct Option is D

Solution and Explanation

Top Questions on Functions

Questions Asked in CAT exam

Let $f(x)=x^2+ax+b$ and $g(x)=f(x+1)-f(x-1)$ . If $f(x)≥0$ for all real $x$ , and $g(20)=72$ , then the smallest possible value of $b$ is