If the zeroes of the quadratic polynomial $x^2+bx+c,\ c
eq0$ are equal, then find $a$ and $c$ have equal signs or opposite?

Given: The zeroes of the quadratic polynomial $x^2+bx+c,\ c\
eq0$ are equal.

To do: To find the sign of the roots of the quadratic polynomial.

Solution:

Given that the zeros of the quadratic polynomial $ax^2+bx+c,\ c\
eq0$ are equal.

$\Rightarrow$  Value of the discriminant $( D)$ has to be zero for equal roots.

$\Rightarrow b^2-4ac=0$

$\Rightarrow b^2=4ac$

Since. L.H.S, $b^2$ cannot be negative, thus, R.H.S. can also be never negative.

Therefore, $a$ and $c$ must be of the same sign.

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Updated on: 10-Oct-2022

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