Question

PCC)=
18. If the product of the zeroes of
C2k-1) x² - 6x-6 is 4, then find value of k​

Answer 1

Answer :

k = -11½

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

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

Solution :

Here ,

The given quadratic polynomial is ;

(2k - 1)x² - 6x - 6

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we get ;

a = 2k - 1

b = -6

c = -6

Also ,

It is given that , the product of zeros of the given quadratic polynomial is 4 .

=> Product of zeros = 4

=> c/a = 4

=> (2k - 1)/(-6) = 4

=> 2k - 1 = 4•(-6)

=> 2k - 1 = -24

=> 2k = -24 + 1

=> 2k = -23

=> k = -23/2

=> k = -11½

Hence , k = -11½