Choose the correct answer from the given four options in the foll…

MCQ

Choose the correct answer from the given four options in the following questions:
If the zeroes of the quadratic polynomial $ax^2 + bx + c, c ≠ 0$ are equal, then:

✓
c and a have opposite signs.
B
c and b have opposite signs.
C
c and a have the same sign.
D
c and b have the same sign.

✓

Answer

Correct option: A.

c and a have opposite signs.

The zeroes of the given quadratic polynomial $ax^2 + bx + c, c ≠ 0$ are equal, if coefficient of $x^2$ and constant term have the same sign i.e., c and a have the same sign. While b i.e., coefficient of x can be positive/negative but not zero.e.g., (i) $x^2+4 x+4=0$
(ii) $x^2-4 x+4=0$
$\Rightarrow(x+2)^2=0 \Rightarrow(x-2)^2=0$
$\Rightarrow x=-2,-2 \Rightarrow x=2,2$
Alternate Answer
Given that, the zeroes of the quadratic polynomial $ax^2 + bx + c$ where c ≠ 0, are equal i.e., discriminant (D) = 0
$\Rightarrow b^2-4 a c=0$
$\Rightarrow b^2+4 a c$
$\Rightarrow a c=\frac{b^2}{4}$
$\Rightarrow a c>0$
Which is olny possible when a and c have the same signs.

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