Question

if 2 and 1/2 are the zeroes of the polynomial p(x)=ax^2+5x+b ,show that a=b

Answer 1

f(x)= ax^2+5x+b

f(2)= a×2×2+5×2+b

4a+10+b=0

4a+b=-10. _. (i)

p(x)= ax^2+5x+bx

p(1/2)= a×1/2×1/2+5×1/2+b×1/2

a/4+5/2+b/2=0

a+10+2b=0

a+2b=-10. _. (ii).

(i) × 2 -. (ii)

(8a+2b)-(a+2b)=(-10)-(-10)

8a+2b-a-2b=-10+10

7a=0

a=0

put the value of a=0 in (i)

4a+b=0

4×0+b=0

b=0

a=b=0

so,. a=b

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Answer 2

Answer:

Step-by-step explanation:

sum of zeros= -b/a (formula)

2+1/2= (-5)/a

5/2=(-5)/a

therefore, a= (-2)

product of zeros =c/a

2*1/2= b/a

1=b/a

therefore, b= (-2)

Hence a=b=(-2)