Question

if the sum of zeroes of a quadratic polynomial 3x²-kx+6 is 3 the value of k is???

Answer 1

Answer:

k = 9

Note:

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

• Zeros of a polynomial are the possible values of unknown (variable) for which the polynomial becomes zero .

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

• A quadratic polynomial has atmost two zero.

• 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 the zeros of any quadratic polynomial, then it is given as ;

x² - (A+B)x + A•B .

Solution:

Here,

The given quadratic polynomial is ;

3x² - kx + 6.

Clearly , we have ;

a = 3

b = -k

c = 6

Also,

It is given that , the sum of zeros of the given quadratic polynomial is 3 .

Thus,

=> Sum of zeros = 3

=> -b/a = 3

=> -(-k)/3 = 3

=> k/3 = 3

=> k = 3•3

=> k = 9

Hence,

The required value of k is 9 .

Moreover,

If k = 9 , then the given quadratic polynomial will be reduced to ; 3x² - 9x + 6 .

Also,

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

Thus,

=> 3x² - 9x + 6 = 0

=> 3(x² - 3x + 2) = 0

=> x² - 3x + 2 = 0

=> x² - x - 2x + 2 = 0

=> x(x - 1) - 2(x - 1) = 0

=> (x - 1)(x - 2) = 0

=> x = 1 , 2

Hence,

The two zeros of the given quadratic polynomial are ; x = 1 , 2 .

Answer 2

$\huge \mathtt{ \fbox{Solution :)}}$

Given ,

• The quadratic eq is 3x²-kx+6

• The sum of roots of quadratic eq is 3

We know that , the sum of roots of quadratic equation is given by

$\large \mathtt{ \fbox{Sum \: of \: roots = - \frac{b}{a} }}$

Thus ,

3 = -(-k/3)

3 = k/3

k = 3 × 3

k = 9

Hence , the value of k is 9

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