Question

2 X + 1 is a factor of x cube + 23 x square + 21 X + 30 find the value of k

Answer 1

Therefore, if x=-1÷2 then f(x)=0
(-1÷2)^3+23×(-1÷2)^2+21×(-1÷2)+30=0
-1÷8+-23÷4+-21÷2+30=0

Answer 2

HERE IS YOUR ANSWER

QUESTON:- KX³+23X²+71X+30

⇒ GIVEN THAT 2X+1 IS A FACTOR

2X+1= 0

2X= 0-1

X= $\frac{-1}{2}$

P(X)= KX³+23X²+71X+30=0

P($\frac{-1}{2}$)= K*(-1/2)³ +23* (-1/2)² + 71 *-1/2 + 30 = 0

= K*-1/8 + 23*1/4 + -71/2 +30 = 0

= -1/8K +23 /4 +-71/2 +30= 0

⇒ TAKE THE LCM OF 23/4, -71/2,30

⇒ LCM=4

= -1/8K + 23*1/4*1 + -71*2/2*2 + 30*4/1*4 = 0

-1/8K + (23 + -142+120)/4= 0

-1/8K + (143 +-142)/4=0

-1/8K + 1 =0

-1/8K = 0-1

-1/8K = -1

K= -1*8/ -1

K= -8/-1

K= 8

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