Question

full explanation.please solve correct answer will explanation I will mark you brainliest.​​

Answer 1

Answer:

k=1

Step-by-step explanation:

f(x)= x²+ax-6

g(x)= x²+bx+2

here, (x+2)=0 therefore x= -2

therefore, +(-2) = (-2)² + (-2)a-6 =0

4-2a-6=0

-2=2a

a= -1 _________equation (1)

g(-2) = (-2)² + (-2)b + 2

4-2b+2=0

6-2b

b=3____________equation(2)

kx²-ax-(a+b)

a = (-1) and b=3

therefore kx²+x-2=0

(x=2) = (-2)²k = -2-2=0

4k=4

k=1

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=1}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies {x}^{2} + ax - 6 = 0 \\ \\ \tt: \implies {ax}^{2} + bx + 2 = 0 \\ \\ \tt: \implies {kx}^{2} - ax - (a + b) = 0 \\ \\ \tt: \implies Common \: factor = x + 2 \\ \\ \red{\underline \bold{To \: Rind : }} \\ \tt: \implies Value \: of \: k=?$

• According to given question :

$\tt \circ \: x + 2 = 0 \implies x = - 2 \\ \\ \bold{As \: we \: know \: that} \\ \tt : \implies p(x) = {x}^{2} + ax - 6 = 0 \\ \\ \tt : \implies p( - 2) =( - 2)^{2} + a \times ( - 2) - 6 = 0 \\ \\ \tt : \implies 4 - 2a - 6 = 0 \\ \\ \tt : \implies 2a = - 2 \\ \\ \green{\tt : \implies a = - 1} \\ \\ \bold{Similarly : } \\ \tt: \implies p(x) = {x}^{2} + bx + 2 = 0 \\ \\ \tt: \implies p( - 2) =( - 2)^{2} + b \times ( - 2) + 2 = 0 \\ \\ \tt: \implies 4 - 2b + 2 = 0 \\ \\ \tt: \implies 2b = 6 \\ \\ \green{\tt: \implies b = 3} \\ \\ \bold{For \: value \: of \: k : } \\ \tt: \implies p(x) = {kx}^{2} - ax - (a + b) = 0 \\ \\ \tt: \implies p( - 2) =k \times ( - 2)^{2} - ( - 1) \times ( - 2) - ( - 1 + 3) = 0 \\ \\ \tt: \implies 4k - 2 - 2 = 0 \\ \\ \tt: \implies 4k = 4 \\ \\ \green{\tt: \implies k = 1} \\ \\ \green{\tt \therefore value \: of \: k \: is \: 1}$