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Question

If x = 0 and x = - 1 are the roots of the polynomial f(x) = 2x33x2 + ax + b, find the value of a and b.


Solution

f(x) = 2x33x2 + ax + b

x = 0 and x = - 1 are its zeros

f (0) = 0 and f(-1) = 0

Now, f(0) = 0

2(0)33(0)2+a× 0 + b = 0

0 - 0 + 0 + b = 0

b = 0

and f(-1) = 0

2(2)33(1)2 + a (-1) + b = 0

2×(1)3×1+a× (-1) + b = 0

-2 - 3 - a + b =0

23a=0 a = - 5

5a=0 a = - 5

Hence a = - 5, b = 0


Mathematics
RD Sharma
Standard IX

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