KVPY SX SB Exam 2016 Question Paper

Question : 5 of 120

Marks: +1, -0

Suppose the tangent to the parabola

y = x^2 + px + q

at (0, 3) has slope –1. Then p + q equals

Solution:

(0, 3) lies on the curve
So q = 3
Now

{dy}/{dx}=2x+p;

({dy}/{dx})_{(0,3)}=p=-1

∴ p + q = –1 + 3 = 2

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