Math, asked by pv439307, 1 month ago

6. The number of polynomials having zeroes as 5 and -3 is (a) (b)2 (C)3 (d) more than 3​

Answers

Answered by illuminati707
4

Let p(x) be the required polynomial, in which zeroes of the polynomial are -2 and 5.

The polynomial is of the form,

p

(x)=a

x 2

+bx+c

p(x)=ax2+bx+c

To find the variables a and b:

Sum of the zeroes =

−b

a

−ba

, where

b is coefficient of

x

x

a is coefficient of

x 2

x2

−2+5=

−b

a

−2+5=−ba

3=

−b

a

3=−ba

Hence,

3

1

=

−b

a

31=−ba

Therefore, the values of a and b is

a=1

a=1

and

b=−3

b=−3

.

Product of the zeroes = constant term ÷ coefficient of x2 i.e.

Product of zeroes =

c

a

ca

, where

c is the constant term.

a is coefficient of

x 2

x2

.

(

−2)5=

c

a

(−2)5=ca

−10=

c

a

−10=ca

Hence,

−10

1

=

c

a

−101=ca

Therefore, the value of c is

−10=c

−10=c

Hence, we got

a=1

a=1

,

b=−3

b=−3

and

c=−10

c=−10

.

Substituting the values of a, b and c in the polynomial

p

(x)=a

x 2

+bx+c

p(x)=ax2+bx+c

p

(x)=1⋅

x 2

−3x−10

p(x)=1⋅x2−3x−10

Therefore, p(x) is

p

(x)=

x 2

−3x−10

p(x)=x2−3x−10

Therefore, we can conclude that x can take any value.

Hence, option D is the correct answer.

thank u for asking

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