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Q.

A certain polynomial, P, has a degree of 2. Polynomial P has zeros of 2 and -3, and a>0when the function of polynomial P is written in the form of y=ax2+bx+c. Given this information, which of the following could be the graph of polynomial P?


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a

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b

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c

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d

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answer is B.

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Detailed Solution

Given that the quadratic polynomial has zeros as 2 -3 the form of quadratic polynomial is ax2+bx+c function of polynomial, y=ax2+bx+c.
This means, at x=2 x=-3, y will be zero i.e, the function will take value as zero.
So, according to options given, option (3) and option (4) can be eliminated.
Since, i.e, a>0, the coefficient of x2 is positive.
At large values of on both sides of 0 (zero), the value of ax2+bx+c will be dominated by ax2, since the term has x2 in it.
So, for large values of x if a>0, therefore, the parabola must open upwards.
Question ImageHence, the answer is option 2.
 
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