Question

if the zeroes od of the quadratic polynomula x2 + (a+1)x+b are 2 and -3 , then find the value of a and b
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Answer 1

x2-5x+k ,

Here, a=1 , b=-5 and c=b

Now, α+ β = -\frac{b}{a}

a

b

= -\frac{-5}{1}

1

−5

= 5

α x β = \frac{c}{a}

a

c

= \frac{b}{7}

7

b

= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4b=1

⇒ -4b= 7-25

⇒ -4b= -24

⇒ b=6 So the value of b is 6.

Answer 2

Step-by-step explanation:

sum of roots of ax^2+bx+c=0 is -b/a

product of roots = c/a

b=a+1, a=1,c=b

sum of roots:

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

-1=-(a+1)

1=a+1

=> a=0

product of roots:

b/1 = 2×(-3)

b=-6

a=0, b=-6