Consider the following statement in respect of the quadratic equation ax2 bx c 0 where I The product...........

Quantitative Aptitude (CDS) Quadratic Equations

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Consider the following statement in respect of the quadratic equation ax²+ bx + c = 0 , where $a\neq 0$ .

I. The product of the root is equal to the sum of the roots.

II. The product of the equation are always unequal and real.

Which of the statement given above is /are correct?

only I

only II

both I and II

neither I nor II

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Explanation:

ax²+bx+b=0
x²+ (b/a) x+ (b/a) =0
Sum of roots ( $\alpha$ + $\beta$ ) = (− b/a)
Product of roots ( $\alpha$ $\beta$ ) = (b/a)
Hence product of the roots is not equal to the sum of root so statement 1 not correct.
Now for roots to be real and unequal
Determinant D>0
⇒ b²- 4ac>0
⇒ b²- 4a (b)>0 ⇒ b²>4ab
b>4a
So, if b>4a then roots are unequal and real, so statement 2 is not always true it will depends on values of a and b