Question

(viii) g(x) = a (x² +1) – x (a? + 1) - a +1​

Answer 1

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>>Quadratic Equations

>>Solutions of Quadratic Equations

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Question

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Find the zeros of each of the following quadratic polynomial and verify the relationship between the zeros and their coefficients :

(i) f(x)=x

2

−2x−8

(ii) g(x)=4s

2

−4s+1

(iii) f(x)=x

2

−(

3

+1)x+

3

(iv) x

2

−3−7x

(v) p(x)=x

2

+2

2

x−6

(vi) q(x)=

3

x

2

+10x+7

3

(vii) g(x)=a(x

2

+1)−x(a

2

+1)

Medium

Solution

verified

Verified by Toppr

ax

2

+bx+c=0⇒α+β=−

a

b

,αβ=

a

c

(i)

x

2

−2x−8=0

⇒a=1,b=−2,c=−8

x

2

−2x−8=0

(x−4)(x+2)=0

α=−2,β=4

α+β=−

a

b

→−2+4=−

1

−2

⇒2=2

αβ=

a

c

→(−2)(4)=

1

−8

⇒−8=−8

Answer 2

Answer:

$g(x) = a(x {}^{2} + 1) - x(a {}^{2} + 1) \\ = ax {}^{2} + a - a {}^{2} x - x.$