Let $f (x) = a x^{2} + b x + c$ . Then, match the following :
$\begin{matrix} a . Sum of roots of f(x) = 0 & 1. - \frac{b}{a} b . Product of roots of f(x) = 0 & 2. \frac{c}{a} c . Roots of f(x) = 0 are real & distinct & 3. b^{2} - 4 a c = 0 d . Roots of f(x) = 0 are real and identical. & 4. b^{2} - 4 a c > 0 \end{matrix}$
The correct matching is -

Join BYJU'S Learning Program

The value of b and c for which the indetityf(x+1)−f(x)=8x+3 is satisfied where f(x)=bx2+cx+d, are

The correct option is B b=4, c=−1Since the the given equality is true ∀x∈R.Put x=0 in given equation,we get b+c=3 .....(i)Now put x=1 in the given equation,we get 3b+c=11 .....(ii)Solving these two equations,b=4 and c=−1

The value of $b$ and $c$ for which the indetity $f (x + 1) - f (x) = 8 x + 3$ is satisfied where $f (x) = b x^{2} + c x + d$ , are

The correct option is B $b = 4$ , $c = - 1$
Since the the given equality is true $\forall x \in R$ .
Put $x = 0$ in given equation,
we get $b + c = 3$ $. . . . . (i)$
Now put $x = 1$ in the given equation,
we get $3 b + c = 11$ $. . . . . (i i)$
Solving these two equations,
$b = 4$ and $c = - 1$