For , let satisfy for all . Also, the equation has only one distinct real solution.…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For

a,b\in\mathbb{R}\setminus\{0\}

, let

f(x)=ax^2+bx+a

satisfy

f\left(x+\frac{7}{4}\right)=f\left(\frac{7}{4}-x\right)

for all

x\in\mathbb{R}

. Also, the equation

f(x)=7x+a

has only one distinct real solution. The value of

a+b

is (a) 4 (b) 5 (c) 6 (d) 7

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