If x = 0 and x = -1 are the roots of the polynomial f (x) = 2x³-3x²+ax+b, find the value of a and b.
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Given : If x = 0 and x = -1 are the roots of the polynomial f(x) = 2x³ - 3x² + ax + b
On putting x = 0 in the given polynomial :
f (0) = 2 (0)³ – 3 (0)² + a (0) + b
f (0) = 2 × 0 - 3 × 0 + 0 + b
f (0) = 0 – 0 + 0 + b
f (0) = b
On putting x = -1 in the given polynomial f(x):
f (-1) = 2 (-1)³ – 3 (-1)² + a (-1) + b
f (-1) = - 2 - 3 - a + b
f (-1) = - 5 - a + b
Since, x = 0 and x = -1 are roo of the polynomial f (x) :
∴ f (0) = 0 and f (-1) = 0
⇒ b = 0 and - 5 – a + b = 0
⇒ a – b = - 5
⇒ a – 0 = - 5
⇒ a = - 5
Hence, the value of a = - 5 and b = 0
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