if X=3and x=1ate the roots of the polnamiol 4(x)=2x3_5x2+ax+b,find the blue of a and b.
Answers
Step-by-step explanation:
Given:-
X = 3 and X = 1 are the roots of the pilynomial P(X)=2X^3-5X^2+aX+b
To find:-
Find the value of 'a' and 'b' ?
Solution:-
Given Pilynomial P(X) = 2X^3-5X^2+aX+b
If X = 3 is the root of P(X) then it satisfies the given Polynomial .i.e. P(3)=0
=>P(3)=2(3)^3-5(3)^2+a(3)+b = 0
=>2(27)-5(9)+3a+b = 0
=>54 -45 + 3a + b = 0
=>9 + 3a + b = 0
=>3a + b = -9 ---------------(1)
If X = 1 is the root of P(X) then it satisfies the given Polynomial .i.e. P(1)=0
=>P(1) = 2(1)^3-5(1)^2+a(1)+b = 0
=>2(1)-5(1)+a+b = 0
=>2 - 5 + a + b = 0
=>-3 + a + b = 0
=> a + b = 3 ----------------(2)
On subtracting (2) from (1)
3a + b = -9
a + b = 3
(-)
_________
2a +0 = -12
__________
=>2a = -12
=>a = -12/2
=>a = -6
On Substituting the value of a in equation (2)
-6+b = 3
=>b = 3+6
=>b = 9
Answer:-
The values of a and b are -6 and 9 respectively.
a = -6
b = 9
Used formula:-
- If a number is a solution or root of a polynomial then it satisfies the given Polynomial.