CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the quadratic polynomial whose zeros are 3 and -4.


Open in App
Solution

Step 1: Define the quadratic polynomial in terms of its zeros

A quadratic polynomial can be expressed using its zeros as follows,

x2-α+βx+αβ ...(i)

Where, α,β are the zeroes (roots) of the quadratic polynomial.

It is given that the zeroes of the required quadratic polynomial are 3 and -4, i.e., α=3 and β=-4

So, the sum of zeroes =α+β=3+-4=3-4=-1

And, the product of zeroes =αβ=3-4=-12

Step 2: Form the quadratic polynomial

Substitute the values of the sum and product of zeroes in equation (i) to get the required quadratic polynomial,

x2-α+βx+αβ

=x2--1x+-12

=x2+1x-12 [--a=+a,+-a=-a]

=x2+x-12

Hence, the required quadratic polynomial is x2+x-12.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon