Question

if one zero of quadratic polynomial 3x²+ kx-2 is -2.then find the value of k.​

Answer 1

Question:

If one zero of a quadratic polynomial 3x² + kx - 2 is -2 , then find the value of k.

Answer:

k = 5

Note:

• The possible values of unknown (variable) for which the polynomial become zero are called its zeros.

• If x = a is a root of any polynomial in x , then the value of polynomial at x = a is zero otherwise it's not a zero of the polynomial.

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

Solution:

Here,

The given quadratic polynomial is 3x² + kx - 2 .

Also,

It is given that -2 is a zero of the given polynomial, hence at x = -2 , the given polynomial must become zero .

Thus,

=> 3(-2)² + k(-2) - 2 = 0

=> 12 - 2k - 2 = 0

=> 10 - 2k = 0

=> 2k = 10

=> k = 10/2

=> k = 5

Hence,

The required value of k is 5 .

Moreover, if k = 5 then the given polynomial will become ; 3x² + 5x - 2 .

Now,

In order to find the other zero , let's equate it to zero .

Thus,

=> 3x² + 5x - 2 = 0

=> 3x² + 6x - x - 2 = 0

=> 3x(x+2) - (x+2) = 0

=> (x+2)(3x-1) = 0

=> x = -2 , 1/3

Hence,

The other zero of the polynomial is 1/3 .

Answer 2

$\huge{\boxed{\red{\star\;Answer}}}$

$\large{\underline{\blue{\star\;Note}}}$

• x = 'a' is said to be a root of the equation if 'a' satisfies the given equation

Given , -2 is a root of the equation $3x^{2}+kx-2=0$

• Substituting the value of root
• f(-2) = 0
• $3(-2)^{2}+k(-2)-2=0$
• $12-2k-2=0$
• 2k = 10
• k = 5

$\large{\boxed{\purple{The\;value\;of\;k=5}}}$