Question

if 2&3 are zeroes of polynomial 3xsquare-2kx+2m find the values of k and m​

Answer 1

$\boxed{\textbf{\large{Step-by-step explanation:}}}$

we have given,

the roots of the equation are

2 and 3

• let, us consider the roots are

α and β

α = 2 , β = 3

• our equation is 3x²-2kx+2m

compare it with ax^2 + bx + c = 0

a = 3 , b = ( -2k ) c = 2m

• we know the relation between coefficients and roots of the equations

α + β = -b / a

Therefor,

→ 2 + 3 = - ( - 2k) / 3

→ 5 = 2k / 3

→ 5 x 3 = 2k

→ 15 /2= K

$\boxed{\textbf{\large{K = 15 /2 = 7.5}}}$

Also,

α x β = c / a

→2 x 3 = 2m / 3

→6 x 3 = 2m

→18 / 2= m

→ 9 = m

$\boxed{\textbf{\large{m = 9}}}$

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Verification :

• put the values of k , m and value of one of the root in the given equation 3x²-2kx+2m And equate the equation with zero

→ 3x²-2kx+2m = 0

→ 3 ( 2 )² - 2 (15 /2) 2 + 2( 9 ) = 0

→ 3 ( 4 ) - 2 x 15 + 18 = 0

→ 12 - 30 + 18 = 0

→ 30 - 30 = 0

hence verified

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