Question

PLEASE ANSWER IT FASTER.​

Answer 1

${\textbf{\large{step by step explanation }}}$

we have given the ratio of roots of quadratic equation is 2:5

let,

α and β are the roots of the given quadratic equation x^2 + kx + 40

α / β = 2/ 5

α = 2x

β = 5x

▶(x^2 + kx + 40 = 0) compare the equation with standard form of quadratic equation ax^2 + bx + c = 0

x^2 + kx + 40 = 0

a = 1 , b = K ,c = 40

we know,

α + β =( -b ) / a

↪ 2x + 5x = -k / 1

↪ 7x = -k ......... .(1)

Now, α x β = c / a

↪ (2x )x (5x )= 40 / 1

↪ 10x^2 = 40

↪ x = √ ( 4 )

x = 2

put value of x in equation (1)

7x = -k

7( 2 ) = -k

$\boxed{\textbf{\large{K = -14}}}$

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Answer 2

answer -: k= -14 ...........