Question

find k if the roots of the quadratic equation x square +kx +4 equal to 0 are in the ratio2:5​

Answer 1

Answer:

alpha=2/√10

k=-7alpha=-7(2/√10)=-14/√10

Answer 2

Given :-

◉ A quadratic equation, x² + kx + 4 = 0 which has its roots in the ratio 2 : 5

To Find :-

◉ Value of k

Solution :-

Let the common factor of both the roots be x, then the roots are 2x and 5x.

Comparing the given quadratic equation with the standard form of quadratic equation i.e., ax² + bx + c = 0, we have

• a = 1 ; b = k ; c = 4

We know,

⇒ Sum of zeroes(roots) = - b/a

⇒ 2x + 5x = -k / 1

⇒ 7x = -k

⇒ x = - k/7 ...(1)

Now, It is also known that

⇒ Product of zeroes = c / a

⇒ 2x × 5x = 4 / 1

⇒ 10x² = 4

⇒ 5x² = 2

⇒ 5×k²/49 = 2 [ from (1) ]

⇒ 5k² = 98

⇒ k = 7√(2 / 5)