CAT Exam Model Paper 7 with solutions for free online practice

Question : 18 of 60

Marks: +1, -0

The graph of y = ax

^{2}

+ bx + c is shown below. If it is given that | α | < | β |, then which of the following is true?

Solution:

As the graph is downward open, so a < 0.
Also, sum of the roots

α+β= {-b}/{a}

is negative 3 (or less than zero).
[Since | α | < | β | and is less than zero]

-b/a<0

So b < 0.
Also, product of the roots is negative as β is negative.
So

αβ = c/a

is negative or

c/a < 0.

So c is positive (or greater than zero).
Hence a < 0, b < 0 and c > 0.

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