if (x-1)is a factor of p(x)=kx2+x-3 what is the value of k?find the other factor of p(x).
Answers
EXPLINATION:
(x - 1) is the factor of the equation,
⇒ p(x) = kx² + x - 3.
As we know that,
x - 1 is the zeroes of the polynomial.
⇒ x - 1 = 0.
⇒ x = 1.
Put the value of x = 1 in equation, we get.
⇒ k(1)² + (1) - 3 = 0.
⇒ k + 1 - 3 = 0.
⇒ k - 2 = 0.
⇒ k:2
INFORMATION
Hence, (x+1) is not a factor of p(x)=6x
3
+3x
2
(b) Let f(x) be the required polynomial.
p(x)=6x
3
+3x
2
Let the first degree polynomial to be added to ax+b.
f(x)=p(x)+ax+b
If x
2
−1 is a factor of the f(x), then f(−1)=0 and f(1)=0
f(−1)=p(−1)+a(−1)+b
⇒0=6(−1)
3
+3(−1)
2
−a+b
⇒0=−6+3−a+b
⇒a−b=−3....(i)
Also, f(1)=p(1)+a(1)+b
⇒0=6(1)
3
+3(1)
2
+a+b
⇒a+b=−9....(ii)
Solving (i) and (ii), we get
a=−6,b=−3
∴ The polynomial is (−6x−3)
รσɭนtıσŋ:-
( x - 1 ) is the factor of the equation,
➛P ( x ) = KX² + X - 3
As we know that,
x - 1 is the zero of the polynomial.
➛x - 1 = 0
➛x = 1
Put the value of x = 1 in equation , we get
➛K ( 1 ) ² + ( 1 ) - 3 = 0
➛K + 1 - 3 = 0
➛K - 2 = 0
➛K = 2
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