Question

In the standard form of quadratic equation shown below, which among a, b and c should not be equal to 0?

ax2+bx+c=0

Answer 1

Answer:

For the quadratic equation ax

2

+bx+c=0,a,b,c,εQ

Roots are given by

α=

2a

−b+

b

2

−4ac

and

β=

2a

−b−

b

2

−4ac

If D=0 then α=

2a

−b

=β i.e. the roots are equal and real.

Since a,b and c∈Q, the roots will be equal and rational.

Hence, statements P and R are correct.

Answer 2

To find:

In the standard form of quadratic equation $ax^{2}+bx+c=0$, which among $a,b$ and $c$ should not be equal to $0$

Step-by-step explanation:

Given, $ax^{2}+bx+c=0$

When $a=0$, we get

$\quad bx+c=0$

This is not a quadratic equation. So $a$ must not be $0$

When $b=0$, we get

$\quad ax^{2}+c=0$

This is a quadratic equation. So $b$ can be $0$.

When $c=0$, we get

$\quad ax^{2}+bx=0$

This is also a quadratic equation. So $c$ can be $0$.

Final answer:

$a$ should not be $0$.