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

MATHEMATICS · Single correct · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

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 real distinct solution. The value of

a+b

is equal to (a)

4

(b)

5

(c)

6

(d)

7

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