Question

If 1/2 is a zero of the polynomial p(x) = 2x3 + ax2 + 11x + a +3, find the
value of a.​

Answer 1

Answer:

2x³+ax²+11x+a+3=0

2*1/8+a*1/4+11*2+a+3=0

1/4+a/4+22+a+3=0

a+1/4+25+a=0

a+1/4+a=-25

a+1+4a/4=-25

5a+1/4=-25

5a+1=-120

5a=-119

a=-119/5

Answer 2

Answer :

a = -7

Solution :

• Note : If x = c is a zero of the polynomial p(x) , then p(c) = 0 .

Here ,

The given polynomial is ;

p(x) = 2x³ + ax² + 11x + a + 3

Also ,

It is given that , x = ½ is a zero of the given polynomial p(x) .

Thus ,

=> p(½) = 0

=> 2•(½)³ + a•(½)² + 11•(½) + a + 3 = 0

=> 1/4 + a/4 + 11/2 + a + 3 = 0

=> (1 + a + 22 + 4a + 12)/4 = 0

=> (5a + 35)/4 = 0

=> 5a + 35 = 0•4

=> 5a + 35 = 0

=> 5a = -35

=> a = -35/5

=> a = -7

Hence a = -7 .