Question

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and coefficients p(t)= 3 t square - 9 t

Answer 1

Question:

Find the zeros of the given quadratic polynomial and verify the relationship between the zeros and coefficients : p(t)= 3t² - 9t.

Answer:

Zeros of the given quadratic polynomial p(t) are :

t = 0 , 3

Note:

• A polynomial of degree 2 is called quadratic polynomial.

• A quadratic polynomial has at most two zeros.

• The possible values of variables for which the polynomial becomes zero are called its zeros.

• In order to find the zeros of a polynomial , equate it to zero.

• The general form of a quadratic polynomial is given as : ax² + bx + c .

• If A and B are the zeros of s quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

• If A and B are given zeros of any quadratic polynomial then that quadratic polynomial is given by : x² - (A+B)x + A•B .

Solution:

Here,

The given quadratic polynomial is :

p(t) = 3t² - 9t

ie ; p(t) = 3t² - 9t + 0

Clearly, we have ;

a = 3

b = -9

c = 0

Now,

Let's find the zerosof the given polynomial p(t) by equating it to zero.

Thus,

=> p(t) = 0

=> 3t² - 9t = 0

=> 3t(t - 3) = 0

=> t(t-3) = 0

=> t = 0 , 3

Hence,

The zeros of the given quadratic polynomial p(t) are : t = 0 , 3 .

Verification of relationship between sum of zeros and coefficients:

Sum of zeros = 0 + 3 = 3

-b/a = -(-9)/3 = 3

Clearly ,

Sum of zeros = -b/a

Verification of relationship between product of zeros and coefficients:

Product of zeros = 0×3 = 0

c/a = 0/3 = 0

Clearly,

Product of zeros = c/a

Hence verified.