Question

if the sum of the zeroes of the quadratic polynomial 3x^2_kx+6 is 3then find the value of k​

Answer 1

Answer:

• Value of k is 9

Explanation:

Given quadratic polynomial is:

• 3 x^2 - k x + 6

Sum of zeroes of given polynomial is 3.

So, As we know

For a given quadratic polynomial ax^2 + bx + c

• Sum of zeroes = -(coefficient of x)/(coefficient of x^2) = -b/a
• Product of zeroes = constant term/coefficient of x^2 = c/a

For the given quadratic polynomial

3 x^2 - k x + 6

• Coefficient of x = -k
• Coefficient of x^2 = 3
• constant term = 6

→ Sum of zeroes = 3

→ - ( coefficient of x ) / coefficient of x^2 = 3

→ -(-k) / 3 = 3

→  k = 3 × 3

→ k =  9

Therefore,

• Value of k is 9.

Answer 2

ɢɪᴠᴇɴ:-

• A quadratic polynomial :- $\tt3 x^2 - k x + 6$
• sum of its zeroes is 3.

ᴛᴏ ғɪɴᴅ:-

• The value of "k".

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

For a quadratic polynomial $\tt ax^2 + bx + c$,

$\tt \dagger \: \: \: \: \: sum \: of \: zeros$

$\tt\alpha + \beta = \dfrac{ - b}{a} = \dfrac{-coefficient \: of \: {x}^{2} }{coefficient \: of \: x}$

$\tt\dagger \: \: \: \: \: product\: of \: zeros.$

$\tt\alpha \beta = \dfrac{ c}{a} = \dfrac{contant \: term }{coefficient \: of \: x}$

Given quadratic polynomial,

$3 x^2 - k x + 6$

Here,

• Coefficient of x = -k
• Coefficient of x^2 = 3
• constant term = 6

Sum of zeroes = 3

$\tt\dfrac{-coefficient \: of \: {x}^{2} }{coefficient \: of \: x}$=3

$\tt\dfrac{ -(-k) }{ 3}$ = 3

 k = 3 × 3

$\pink{ \underline{ \boxed{ \sf{k=9}}}}$

Hence, the value of k is 9.

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