Question

form the quadratic polynomials whose zeroes are (A) 3 and 1/4 (B)1/p and 1/q (C)-9 and -1/9 Please help me with this question

Answer 1

Note:

I have taken:

Alpha=a

Beeta=b

Let the roots be a and b.

A) Given:

a=3

b=1/4

To Find:

Quadratic polynomial=?

Solution:

Formula:

x²-(a+b) x+ab=0

• Sum of the roots=a+b

=3+1/4

=12+1/4

=13/4

• Product of the roots=ab

=3×1/4

=3/4

By substituting the values in the required formula we get,

x²-13/4x+3/4=0.....(As a quadratic equation)

B) Given:

a=1/p

b=1/q

To Find:

Quadratic polynomial=?

Solution:

Formula:

x²-(a+b) x+ab=0

•Sum of the roots=1/p+1/q

=q+p/pq

• Product of the roots =ab

=1/p×1/q

=1/pq

Now, By substituting the values in the formula we get

x²-q+p/pqx+1/pq=0......(As a required quadratic polynomial)

C) Given:

a=-9

b= -1/9

To Find:

Quadratic polynomial=?

Solution:

Formula:

x²-(a+b) x-ab=0

So,

•Sum of the roots=a+b

=-9+(-1/9)

=-9-1/9

= -81-1/9

= -82/9

• Product of the roots=ab

=-9×-1/9

=9/9

=1

Now, Substituting the values in the formula we get,

x²-82/9+1=0.... (As a required quadratic equation)

Hope it will help you !

#Siddhi