Question

find the value of k,if the roots of the quadratic equation x square +kx+40=0 are in the ratio 2:5.

Answer 1

Step-by-step explanation:

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Answer 2

The value of k is 14 or -14

Solution:

Given equation is:

$x^2 + kx+40=0$

Compare the above equation with $ax^2+bx+c=0$, we get

a = 1

b = k

c = 40

We know that,

$Sum\ of\ roots = \frac{-b}{a}\\\\Sum\ of\ roots = \frac{-k}{1}\\\\Sum\ of\ roots = -k$

Then,

$Product\ of\ roots = \frac{c}{a} \\\\Product\ of\ roots = \frac{40}{1}\\\\Product\ of\ roots = 40$

Roots of equation are in ratio 2 : 5

Let one root be 2x

Let the other root be 5x

Sum of roots = 2x + 5x

Sum of roots = 7x

Then,

-k = 7x

k = -7x

$x = \frac{-k}{7}$

Then,

$Product\ of\ roots = 2x \times 5x \\\\Product\ of\ roots = 10x^2\\\\40 = 10x^2$

$40 = 10 \times ( \frac{-k}{7})^2\\\\40 = 10 \times \frac{k^2}{49}\\\\k^2 = 196\\\\k = \pm 14$

Thus the value of k is 14 or -14

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