Question

pls answer it pls answer it​

Answer 1

Answer :

k = 9

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 ;

p(x) = 3x² - 12x + k

Now ,

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

a = 3

b = -12

c = k

Also ,

It is given that , α and ß are the zeros of the given quadratic polynomial .

Thus ,

• Sum of zeros , (α + ß) = -b/a = -(-12)/3 = 4

• Product of zeros , (αß) = c/a = k/3

Also ,

It is given that , (α - ß) = 2

Now ,

We know that , (A - B)² = (A + B)² - 4AB

Thus ,

=> (α - ß)² = (α + ß)² - 4αß

=> 2² = 4² - 4•(k/3)

=> 4 = 16 - 4k/3

=> 4k/3 = 16 - 4

=> 4k/3 = 12

=> k = 12•(3/4)

=> k = 3•3

=> k = 9

Hence , k = 9 .