Question

if the sum pf the zeros of the quadratic polynomial 3x^2-kx +6 is 3 . then find the value of k​

Answer 1

☯︎ Aɴsᴡᴇʀ

we have a quadratic polynomial,

• 3x² - Kx + 6 = 0
• sum of zeroes = 3

firstly compare the polynomial with, ax² + bx + c = 0

here, 3x² - Kx + 6 = 0

• a = 3
• b = -k
• c = 6

we know that,

$\boxed{ \boxed{ \bold{sum \: of \: zeroes = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} } }}}$

here,

• coefficient of x² = 3
• coefficient of x = -k
• constant term = 6
• and sum of zeroes = 3

then,

$\bold{ : \implies 3 = \frac{ - ( - k)}{3} } \\ \\ \bold{ : \implies \: 3 \times 3 = k} \: \: \\ \\ \bold{ : \implies 9 = k} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \boxed{ \bold{k = 9}} } \: \: \: \: \: \: \: \:$

hence, value of k is 9

__________________________

★ for more informative

$\boxed{ \boxed{ \bold{product \: of \: zeroes = \frac{ constant \: term}{coefficient \: of \: {x}^{2} } }}}$

Answer 2

Aɴsᴡᴇʀ⤵

we have a quadratic polynomial,

3x² - Kx + 6 = 0

sum of zeroes = 3

• firstly compare the polynomial with, ax² + bx + c = 0
• here, 3x² - Kx + 6 = 0
• a = 3
• b = -k
• c = 6

we know that,

$\boxed{ \boxed{ \bold{sum \: of \: zeroes = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} } }}}$

here,

• coefficient of x² = 3
• coefficient of x = -k
• constant term = 6
• and sum of zeroes = 3

then,

$\bold{ : \implies 3 = \frac{ - ( - k)}{3} } \\ \\ \bold{ : \implies \: 3 \times 3 = k} \: \: \\ \\ \bold{ : \implies 9 = k} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \boxed{ \bold{k = 9}} } \: \: \: \: \: \: \: \:$

hence, value of k is 9

__________________________

★ for more informative

$\boxed{ \boxed{ \bold{product \: of \: zeroes = \frac{ constant \: term}{coefficient \: of \: {x}^{2} } }}}$