if -2 and 3 are the zeroes of the polynomial p(x)2x3-x2+ax+b then find the values of a and b
Answers
S O L U T I O N :
We have cubic polynomial p(x) = 2x³ - x² + ax + b & zero of the polynomial p(x) = 0.
Given, two zeroes are -2 & 3, so putting the place of p(x), according to the question;
p(x) = 0
→ p(x) = 2x³ - x² + ax + b = 0
→ 2(-2)³ - (-2)² + a(-2) + b = 0
→ 2 × (-8) - 4 + (-2a) + b = 0
→ -16 - 4 - 2a + b = 0
→ -20 - 2a + b = 0
→ -2a + b = 20
→ b = 20 + 2a ................(1)
Again,
→ p(x) = 2x³ - x² + ax + b = 0
→ 2(3)³ - (3)² + a(3) + b = 0
→ 2 × 27 - 9 + 3a + b = 0
→ 54 - 9 + 3a + b = 0
→ 45 + 3a + b = 0
→ 3a + b = -45
→ 3a + 20 + 2a = -45 [from (1)]
→ 5a + 20 = -45
→ 5a = -45 - 20
→ 5a = -65
→ a = -65/5
→ a = -13
Putting the value of a in equation (1),we get;
→ b = 20 + 2(-13)
→ b = 20 + (-26)
→ b = 20 - 26
→ b = -6
Thus,
The value of a & b will be -13 & -6 .
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