Question

find the zeros of t²-2t_15. Also verify the relationship between zeroes and its coefficient

Answer 1

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution :

Here ,

The given quadratic polynomial is ;

t² - 2t - 15 .

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial at² + bt + c , we have ;

a = 1

b = -2

c = -15

Firstly ,

Let's find the zeros of the given quadratic polynomial by equating it to zero .

Thus ,

=> t² - 2t - 15 = 0

=> t² - 5t + 3t - 15 = 0

=> t(t - 5) + 3(t - 5) = 0

=> (t - 5)(t + 3) = 0

=> t = 5 , -3

Now ,

• Sum of zeros = 5 + (-3) = 5 - 3 = 2

• -b/a = -(-2)/1 = 2

Clearly ,

Sum of zeros = -b/a

Also ,

• Product of zeros = 5×(-3) = -15

• c/a = -15/1 = -15

Clearly ,

Product of zeros = c/a

Hence verified .