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Question

Find the value of a+b+c, if points (−3,10),(0,1) and (2,15) lie on the curve y=ax2+bx+c.

A
6
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B
4
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C
8
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D
5
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Solution

The correct option is A 6
y=ax2+bx+c
Three points (3,10),(0,1),(2,15) lie on the curve.
Substituting them into the curve, we get
10=9a3b+c...(1)
1=c...(2)
15=4a+2b+c...(3)
Substituting value of c from equation 2 in equations 1 and 3, we have
10=9a3b+1 or 3=3ab...(4)
15=4a+2b+1 or 7=2a+b...(5)
Adding equations (4) and (5), we have
10=5a or a=2
And therefore, b=3
a+b+c=2+3+1=6

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