Question

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

• A. $a\to 2;b\to 1;c\to 3;d\to 4$
• B. $a\to 1;b\to 2;c\to 4;d\to 3$
• C. $a\to 3;c\to 4;b\to 2;d\to 1$
• D. $a\to 1;b\to 2;c\to 3;d\to 4$

Answer 1

The correct option is B

$a\to 1;b\to 2;c\to 4;d\to 3$

For f(x) = $a{x}^2+bx+c$.

a. Sum of roots of f(x) = 0 is –$\frac{b}{a}$

b. Product of roots of f(x) = 0 is $\frac{c}{a}$

c. Roots of f(x) = 0 are real & distinct, D= $b^2–4ac>0$

d. Roots of f(x) = 0 are real and equal, D= $b^2–4ac=0$