if0 and 1 are the zeroes of the polynomial S(x) = 2x^3 - 3x^2 + ax + b, find the values<br />of a and b.
Answers
Answered by
2
Given,
f(x)=2x
3
−3x
2
+ax+b
Roots x=0,1
f(0)=0⇒2(0)
3
−3(0)
2
+a(0)+b=0⇒b=0
f(1)=0⇒2(1)
3
−3(1)
2
+a(1)+0=0⇒−1+a=0⇒a=1
∴a=1,b=0
Answered by
0
Step-by-step explanation:
Given : -
- the zeroes of the polynomial S(x) = 2x^3 - 3x^2 + ax + b,
.To Find : -
- find the values of a and b.
Solution : -
f(0) = 0 and f(1) = 0
✪ substitute all values :✪
➻ f(0) = 2(0)³ - 3(0)² + a(0) + b = 0
➻ b = 0.......(1)
f(1) = 2(1)³ - 3(1)² + a(1) + b = 0
✪ Substitute all values :✪
➻ 2 - 3 + a + b = 0
➻ a + b - 1 = 0
➻ a + b = 1 ........(2)
from equations (1) and (2),
a + b = 1
b = 0
________
a = 1
hence, value of a = 1 and b = 0
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